EX-10.2





 Exhibit 10.2 

INVESTMENT MANAGEMENT TRUST AGREEMENT 

This Investment Management Trust Agreement (this “Agreement”) is made effective as of February 26, 2021 by and
between Hudson Executive Investment Corp. III, a Delaware corporation (the “Company”), and Continental Stock Transfer & Trust Company, a New York corporation (the “Trustee”). 

WHEREAS, the Company’s registration statements on Form S-1 (File numbers 333-252744 and 333-253427) (collectively, the “Registration Statement”) and prospectus (the “Prospectus”) for the initial
public offering (the “Offering”) of the Company’s units (the “Units”), each of which consists of one share of the Company’s Class A common stock, par value $0.0001 per share (the
“Common Stock”), and one-fifth of one redeemable warrant, has been declared effective as of the date hereof by the U.S. Securities and Exchange Commission; and 

WHEREAS, the Company has entered into an Underwriting Agreement (the “Underwriting Agreement”) with Citigroup Global
Markets Inc., J.P. Morgan Securities LLC and Barclays Capital Inc., as representatives (the “Representatives”) of the several underwriters (the “Underwriters”) named therein; and 

WHEREAS, as described in the Prospectus, $525,000,000 of the gross proceeds of the Offering and sale of the Private Placement Warrants (as
defined in the Underwriting Agreement) (or $603,750,000 if the Underwriters’ over-allotment option is exercised in full) will be delivered to the Trustee to be deposited and held in a segregated trust account located at all times in the United
States (the “Trust Account”) for the benefit of the Company and the holders of the Common Stock included in the Units issued in the Offering as hereinafter provided (the amount to be delivered to the Trustee (and any interest
subsequently earned thereon) is referred to herein as the “Property,” the stockholders for whose benefit the Trustee shall hold the Property will be referred to as the “Public Stockholders,” and
the Public Stockholders and the Company will be referred to together as the “Beneficiaries”); 
 WHEREAS, pursuant
to the Underwriting Agreement, a portion of the Property equal to $18,375,000, or $21,131,250 if the Underwriters’ over-allotment option is exercised in full, is attributable to deferred underwriting discounts and commissions that will be
payable by the Company to the Underwriters upon and concurrently with the consummation of the Business Combination (as defined below) (the “Deferred Discount”); and 

WHEREAS, the Company and the Trustee desire to enter into this Agreement to set forth the terms and conditions pursuant to which the Trustee
shall hold the Property. 
 NOW THEREFORE, IT IS AGREED: 

1. Agreements and Covenants of Trustee. The Trustee hereby agrees and covenants to: 

(a) Hold the Property in trust for the Beneficiaries in accordance with the terms of this Agreement in the Trust Account established by the
Trustee in the United States at J.P. Morgan Chase Bank, N.A. (or at another U.S. chartered commercial bank with consolidated assets of $100 billion or more) in the United States, maintained by the Trustee and at a brokerage institution selected
by the Trustee that is reasonably satisfactory to the Company; 

  
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 (b) Manage, supervise and administer the Trust Account subject to the terms and conditions
set forth herein; 
 (c) In a timely manner, upon the written instruction of the Company, invest and reinvest the Property solely in United
States government securities within the meaning of Section 2(a)(16) of the Investment Company Act of 1940, as amended, having a maturity of 185 days or less, or in money market funds meeting the conditions of paragraphs (d)(1), (d)(2), (d)(3)
and (d)(4) of Rule 2a-7 promulgated under the Investment Company Act of 1940, as amended (or any successor rule), which invest only in direct U.S. government treasury obligations, as determined by the Company;
it being understood that the Trust Account will earn no interest while account funds are uninvested awaiting the Company’s instructions hereunder and the Trustee may earn bank credits or other consideration; 

(d) Collect and receive, when due, all interest or other income arising from the Property, which shall become part of the
“Property,” as such term is used herein; 
 (e) Promptly notify the Company and the Representatives of all communications received
by the Trustee with respect to any Property requiring action by the Company; 
 (f) Supply any necessary information or documents as may be
requested by the Company (or its authorized agents) in connection with the Company’s preparation of the tax returns relating to assets held in the Trust Account; 

(g) Participate in any plan or proceeding for protecting or enforcing any right or interest arising from the Property if, as and when
instructed by the Company to do so; 
 (h) Render to the Company monthly written statements of the activities of, and amounts in, the Trust
Account reflecting all receipts and disbursements of the Trust Account; 
 (i) Commence liquidation of the Trust Account only after and
promptly after (x) receipt of, and only in accordance with, the terms of a letter from the Company (“Termination Letter”) in a form substantially similar to that attached hereto as either Exhibit A or Exhibit
B, as applicable, signed on behalf of the Company by its Chief Executive Officer, Chief Financial Officer, President, Executive Vice President, Vice President, Secretary or Chairman of the board of directors of the Company (the
“Board”) or other authorized officer of the Company, and, in the case of Exhibit A, acknowledged and agreed to by the Representatives, and complete the liquidation of the Trust Account and distribute the Property in the Trust
Account, including interest earned on the funds held in the Trust Account and not previously released to the Company to pay its taxes (less up to $100,000 of interest to pay dissolution expenses), only as directed in the Termination Letter and the
other documents referred to therein, or (y) upon the date which is, the later of (1) 24 months after the closing of the Offering and (2) such later date as may be approved by the Company’s stockholders in accordance with the
Company’s amended and restated certificate of incorporation if a Termination Letter has not been received by the Trustee prior to such date, in which case the Trust Account shall be liquidated in accordance with the procedures set forth in the
Termination Letter attached as Exhibit B and the Property in the Trust Account, including interest earned on the funds held in the Trust Account and not previously released to the Company to pay its taxes (less up to $100,000 of interest to
pay dissolution expenses), shall be distributed to the Public Stockholders of record as of such date; 

  
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 (j) Upon written request from the Company, which may be given from time to time in a form
substantially similar to that attached hereto as Exhibit C (a “Tax Payment Withdrawal Instruction”), withdraw from the Trust Account and distribute to the Company the amount of interest earned on the Property requested
by the Company to cover any tax obligation owed by the Company as a result of assets of the Company or interest or other income earned on the Property, which amount shall be delivered directly to the Company by electronic funds transfer or other
method of prompt payment, and the Company shall forward such payment to the relevant taxing authority, so long as there is no reduction in the principal amount per share initially deposited in the Trust Account; provided, however, that
to the extent there is not sufficient cash in the Trust Account to pay such tax obligation, the Trustee shall liquidate such assets held in the Trust Account as shall be designated by the Company in writing to make such distribution (it being
acknowledged and agreed that any such amount in excess of interest income earned on the Property shall not be payable from the Trust Account). The written request of the Company referenced above shall constitute presumptive evidence that the Company
is entitled to said funds, and the Trustee shall have no responsibility to look beyond said request; 
 (k) Upon written request from the
Company, which may be given from time to time in a form substantially similar to that attached hereto as Exhibit D (a “Stockholder Redemption Withdrawal Instruction”), the Trustee shall distribute on behalf of the
Company the amount requested by the Company to be used to redeem shares of Common Stock from Public Stockholders properly submitted in connection with a stockholder vote to approve an amendment to the Company’s amended and restated certificate
of incorporation to modify the substance or timing of the Company’s obligation to redeem 100% of shares of Common Stock included in the Units sold in the Offering (the “public shares”) if the Company has not consummated
an initial Business Combination within such time as is described in the Company’s amended and restated certificate of incorporation or with respect to any other material provisions relating to stockholders’ rights or pre-initial Business Combination activity. The written request of the Company referenced above shall constitute presumptive evidence that the Company is entitled to distribute said funds, and the Trustee shall have
no responsibility to look beyond said request; and 
 (l) Not make any withdrawals or distributions from the Trust Account other than
pursuant to Section 1(i), (j) or (k) above. 
 2. Agreements and Covenants of the Company. The Company hereby agrees and
covenants to: 
 (a) Give all instructions to the Trustee hereunder in writing, signed by the Company’s Chairman of the Board, Chief
Executive Officer, Chief Financial Officer, President, Executive Vice President, Vice President or Secretary. In addition, except with respect to its duties under Sections 1(i), 1(j) and 1(k) hereof, the Trustee shall be
entitled to rely on, and shall be protected in relying on, any verbal or telephonic advice or instruction which it, in good faith and with reasonable care, believes to be given by any one of the persons authorized above to give written instructions,
provided that the Company shall promptly confirm such instructions in writing; 

  
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 (b) Subject to Section 4 hereof, hold the Trustee harmless and
indemnify the Trustee from and against any and all expenses, including reasonable counsel fees and disbursements, or losses suffered by the Trustee in connection with any action taken by it hereunder and in connection with any action, suit or other
proceeding brought against the Trustee involving any claim, or in connection with any claim or demand, which in any way arises out of or relates to this Agreement, the services of the Trustee hereunder, or the Property or any interest earned on the
Property, except for expenses and losses resulting from the Trustee’s gross negligence, fraud or willful misconduct. Promptly after the receipt by the Trustee of notice of demand or claim or the commencement of any action, suit or proceeding,
pursuant to which the Trustee intends to seek indemnification under this Section 2(b), it shall notify the Company in writing of such claim (hereinafter referred to as the “Indemnified Claim”). The
Trustee shall have the right to conduct and manage the defense against such Indemnified Claim; provided that the Trustee shall obtain the consent of the Company with respect to the selection of counsel, which consent shall not be unreasonably
withheld. The Trustee may not agree to settle any Indemnified Claim without the prior written consent of the Company, which such consent shall not be unreasonably withheld. The Company may participate in such action with its own counsel; 

(c) Pay the Trustee the fees set forth on Schedule A hereto, including an initial acceptance fee, annual administration fee, and
transaction processing fee which fees shall be subject to modification by the parties from time to time. It is expressly understood that the Property shall not be used to pay such fees unless and until it is distributed to the Company pursuant to
Sections 1(i) through 1(j) hereof. The Company shall pay the Trustee the initial acceptance fee and the first annual administration fee at the consummation of the Offering. The Company shall not be responsible for any other fees or
charges of the Trustee except as set forth in this Section 2(c), Schedule A and as may be provided in Section 2(b) hereof; 

(d) In connection with any vote of the Company’s stockholders regarding a merger, capital stock exchange, asset acquisition, stock
purchase, reorganization or similar business combination involving the Company and one or more businesses (the “Business Combination”), provide to the Trustee an affidavit or certificate of the inspector of elections for the
stockholder meeting verifying the vote of such stockholders regarding such Business Combination; 
 (e) Provide the Representatives with a
copy of any Termination Letter(s) and/or any other correspondence that is sent to the Trustee with respect to any proposed withdrawal from the Trust Account promptly after it issues the same; 

(f) Unless otherwise agreed between the Company and the Representatives, ensure that any Instruction Letter (as defined in Exhibit A)
delivered in connection with a Termination Letter in the form of Exhibit A expressly provides that the Deferred Discount is paid directly to the account or accounts directed by the Representatives on behalf of the Underwriters prior to any transfer
of the funds held in the Trust Account to the Company or any other person; 
 (g) Instruct the Trustee to make only those distributions that
are permitted under this Agreement, and refrain from instructing the Trustee to make any distributions that are not permitted under this Agreement; and 

  
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 (h) Within four (4) business days after the Underwriters exercise the over-allotment
option (or any unexercised portion thereof) or such over-allotment option expires, provide the Trustee with a notice in writing of the total amount of the Deferred Discount. 

3. Limitations of Liability. The Trustee shall have no responsibility or liability to: 

(a) Imply obligations, perform duties, inquire or otherwise be subject to the provisions of any agreement or document other than this Agreement
and that which is expressly set forth herein; 
 (b) Take any action with respect to the Property, other than as directed in
Section 1 hereof, and the Trustee shall have no liability to any third party except for liability arising out of the Trustee’s gross negligence, fraud or willful misconduct; 

(c) Institute any proceeding for the collection of any principal and income arising from, or institute, appear in or defend any proceeding of
any kind with respect to, any of the Property unless and until it shall have received instructions from the Company given as provided herein to do so and the Company shall have advanced or guaranteed to it funds sufficient to pay any expenses
incident thereto; 
 (d) Refund any depreciation in principal of any Property; 

(e) Assume that the authority of any person designated by the Company to give instructions hereunder shall not be continuing unless provided
otherwise in such designation, or unless the Company shall have delivered a written revocation of such authority to the Trustee; 
 (f) The
other parties hereto or to anyone else for any action taken or omitted by it, or any action suffered by it to be taken or omitted, in good faith and in the Trustee’s best judgment, except for the Trustee’s gross negligence, fraud or
willful misconduct. The Trustee may rely conclusively and shall be protected in acting upon any order, notice, demand, certificate, opinion or advice of counsel (including counsel chosen by the Trustee, which counsel may be the Company’s
counsel), statement, instrument, report or other paper or document (not only as to its due execution and the validity and effectiveness of its provisions, but also as to the truth and acceptability of any information therein contained) which the
Trustee believes, in good faith and with reasonable care, to be genuine and to be signed or presented by the proper person or persons. The Trustee shall not be bound by any notice or demand, or any waiver, modification, termination or rescission of
this Agreement or any of the terms hereof, unless evidenced by a written instrument delivered to the Trustee, signed by the proper party or parties and, if the duties or rights of the Trustee are affected, unless it shall give its prior written
consent thereto; 
 (g) Verify the accuracy of the information contained in the Registration Statement; 

(h) Provide any assurance that any Business Combination entered into by the Company or any other action taken by the Company is as
contemplated by the Registration Statement; 

  
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 (i) File information returns with respect to the Trust Account with any local, state or
federal taxing authority or provide periodic written statements to the Company documenting the taxes payable by the Company, if any, relating to any interest income earned on the Property; 

(j) Prepare, execute and file tax reports, income or other tax returns and pay any taxes with respect to any income generated by, and
activities relating to, the Trust Account, regardless of whether such tax is payable by the Trust Account or the Company, including, but not limited to, tax obligations, except pursuant to Section 1(j) hereof; or 

(k) Verify calculations, qualify or otherwise approve the Company’s written requests for distributions pursuant to Sections 1(i),
1(j) or 1(k) hereof. 
 4. Trust Account Waiver. The Trustee has no right of
set-off or any right, title, interest or claim of any kind (“Claim”) to, or to any monies in, the Trust Account, and hereby irrevocably waives any Claim to, or to any monies in, the
Trust Account that it may have now or in the future. In the event the Trustee has any Claim against the Company under this Agreement, including, without limitation, under Section 2(b) or
Section 2(c) hereof, the Trustee shall pursue such Claim solely against the Company and its assets outside the Trust Account and not against the Property or any monies in the Trust Account. 

5. Termination. This Agreement shall terminate as follows: 

(a) If the Trustee gives written notice to the Company that it desires to resign under this Agreement, the Company shall use its reasonable
efforts to locate a successor trustee, pending which the Trustee shall continue to act in accordance with this Agreement. At such time that the Company notifies the Trustee that a successor trustee has been appointed and has agreed to become subject
to the terms of this Agreement, the Trustee shall transfer the management of the Trust Account to the successor trustee, including but not limited to the transfer of copies of the reports and statements relating to the Trust Account, whereupon this
Agreement shall terminate; provided, however, that in the event that the Company does not locate a successor trustee within ninety (90) days of receipt of the resignation notice from the Trustee, the Trustee may submit an
application to have the Property deposited with any court in the State of New York or with the United States District Court for the Southern District of New York and upon such deposit, the Trustee shall be immune from any liability whatsoever; or

 (b) At such time that the Trustee has completed the liquidation of the Trust Account and its obligations in accordance with the
provisions of Section 1(i) hereof and distributed the Property in accordance with the provisions of the Termination Letter, this Agreement shall terminate except with respect to Section 2(b). 

6. Miscellaneous. 
 (a)
The Company and the Trustee each acknowledge that the Trustee will follow the security procedures set forth below with respect to funds transferred from the Trust Account. The Company and the Trustee will each restrict access to confidential
information relating to such security procedures to authorized persons. Each party must notify the other party immediately if it has reason to believe unauthorized persons may have obtained access to such confidential information, or of any change
in its authorized personnel. In executing funds transfers, the 

  
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Trustee shall rely upon all information supplied to it by the Company, including, account names, account numbers, and all other identifying information relating to a Beneficiary,
Beneficiary’s bank or intermediary bank. Except for any liability arising out of the Trustee’s gross negligence, fraud or willful misconduct, the Trustee shall not be liable for any loss, liability or expense resulting from any error in
the information or transmission of the funds. 
 (b) This Agreement shall be governed by and construed and enforced in accordance with the
laws of the State of New York. This Agreement may be executed in several original or facsimile counterparts, each one of which shall constitute an original, and together shall constitute but one instrument. 

(c) This Agreement contains the entire agreement and understanding of the parties hereto with respect to the subject matter hereof. Subject to
Section 6(d) hereof, this Agreement or any provision hereof may only be changed, amended or modified (other than to correct a typographical error) by a writing signed by each of the parties hereto. 

(d) This Agreement or any provision hereof may only be changed, amended or modified pursuant to Section 6(c) hereof with the Consent of
the Stockholders. For purposes of this Section 6(d), the “Consent of the Stockholders” means receipt by the Trustee of a certificate from the inspector of elections of the stockholder meeting certifying that the Company’s
stockholders of record as of a record date established in accordance with Section 213(a) of the Delaware General Corporation Law, as amended (“DGCL”) (or any successor rule), who hold sixty-five percent (65%) or more of all then
outstanding shares of the Common Stock and Class B common stock, par value $0.0001 per share, of the Company voting together as a single class, have voted in favor of such change, amendment or modification. No such amendment will affect any
Public Stockholder who has otherwise indicated his election to redeem his shares of Common Stock in connection with a stockholder vote sought to amend this Agreement to modify the substance or timing of the Company’s obligation to redeem 100%
of the Common Stock if the Company does not complete its initial Business Combination within the time frame specified in the Company’s amended and restated certificate of incorporation. Except for any liability arising out of the Trustee’s
gross negligence, fraud or willful misconduct, the Trustee may rely conclusively on the certification from the inspector or elections referenced above and shall be relieved of all liability to any party for executing the proposed amendment in
reliance thereon. 
 (e) The parties hereto consent to the jurisdiction and venue of any state or federal court located in the City of New
York, State of New York, for purposes of resolving any disputes hereunder. AS TO ANY CLAIM, CROSS-CLAIM OR COUNTERCLAIM IN ANY WAY RELATING TO THIS AGREEMENT, EACH PARTY WAIVES THE RIGHT TO TRIAL BY JURY. 

(f) Any notice, consent or request to be given in connection with any of the terms or provisions of this Agreement shall be in writing and
shall be sent by express mail or similar private courier service, by certified mail (return receipt requested), by hand delivery or by electronic mail: 

  
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 if to the Trustee, to: 

Continental Stock Transfer & Trust Company 

1 State Street, 30th Floor 
 New
York, New York 10004 
 Attn: Francis Wolf & Celeste Gonzalez 

Email: fwolf@continentalstock.com 

Email: cgonzalez@continentalstock.com 

if to the Company, to: 
 Hudson
Executive Investment Corp. III 
 570 Lexington Avenue, 35th Floor 

New York, NY 10022 
 Attn: Douglas
L. Braunstein 
 Email: Douglas.Braunstein@hudsonexecutive.com 

in each case, with copies to: 

Milbank LLP 
 55 Hudson Yards

 New York, New York 10001 

Attn: Rod Miller, Esq. Email: rdmiller@milbank.com 

and 
 Citigroup Global Markets
Inc. 
 388 Greenwich Street 

New York, New York 10013 

Attention: General Counsel 
 and

 J.P. Morgan Securities LLC 

383 Madison Avenue 
 New York, New
York 10179 
 Attention: Equity Syndicate Desk 

and 
 Barclays Capital Inc. 

745 Seventh Avenue 
 New York, New
York 10019 
 Attention: Director of Litigation, Office of the General Counsel 

and 
 Kirkland & Ellis
LLP 
 601 Lexington Avenue New York, NY 10022 

Attn.: Christian Nagler 
 Email:
cnagler@kirkland.com 

  
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 (g) Each of the Company and the Trustee hereby represents that it has the full right and
power and has been duly authorized to enter into this Agreement and to perform its respective obligations as contemplated hereunder. The Trustee acknowledges and agrees that it shall not make any claims or proceed against the Trust Account,
including by way of set-off, and shall not be entitled to any funds in the Trust Account under any circumstance. 

(h) This Agreement is the joint product of the Trustee and the Company and each provision hereof has been subject to the mutual consultation,
negotiation and agreement of such parties and shall not be construed for or against any party hereto. 
 (i) This Agreement may be executed
in any number of counterparts, each of which shall be deemed to be an original, but all such counterparts shall together constitute one and the same instrument. Delivery of a signed counterpart of this Agreement by facsimile or electronic
transmission shall constitute valid and sufficient delivery thereof. 
 (j) Each of the Company and the Trustee hereby acknowledges and
agrees that the Representatives on behalf of the Underwriters are third- party beneficiaries of this Agreement. 
 (k) Except as specified
herein, no party to this Agreement may assign its rights or delegate its obligations hereunder to any other person or entity. 

[Signature Page Follows] 

  
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 IN WITNESS WHEREOF, the parties have duly executed this Investment Management Trust Agreement as of
the date first written above. 
  

			
	CONTINENTAL STOCK TRANSFER & TRUST COMPANY, as Trustee
		
	By:	 	 /s/ Francis Wolf

		 	Name: Francis Wolf
		 	Title: Vice President
	
	HUDSON EXECUTIVE INVESTMENT CORP. III
		
	By:	 	 /s/ Jonathan Dobres

		 	 Name: Jonathan Dobres
 Title: Chief Financial
Officer



 [Signature Page to Investment Management Trust Agreement] 












 SCHEDULE A 
  

							
	 Fee Item
	  	 Time and method of payment
	  	Amount	 
	 Initial set-up fee.
	  	Initial closing of Offering by wire transfer.	  	$	3,500.00	 
	 Trustee administration fee
	  	Payable annually. First year fee payable, at initial closing of Offering by wire transfer, thereafter by wire transfer or check.	  	$	10,000.00	 
	 Transaction processing fee for disbursements to Company under Sections 1 and 2
	  	Billed to Company following disbursement made to Company under Section 1 and 2	  	$	250.00	 
	 Paying Agent services as required pursuant to Section 1(i) and 1(k)
	  	Billed to Company upon delivery of service pursuant to Section 1(i) and 1(k)	  	 
	Prevailing
rates	 
 













 EXHIBIT A 

[Letterhead of Company] 

[Insert date] 
 Continental Stock
Transfer & Trust Company 1 State Street, 30th Floor New York, New York 10004 Attn: Francis Wolf & Celeste Gonzalez 
 Re:
Trust Account Termination Letter 
 Dear Mr. Wolf and Ms. Gonzalez: 

Pursuant to Section 1(i) of the Investment Management Trust Agreement between Hudson Executive
Investment Corp. III (the “Company”) and Continental Stock Transfer & Trust Company (“Trustee”), dated as of __________________ (the “Trust Agreement”), this is to
advise you that the Company has entered into an agreement with (the “Target Business”) to consummate a business combination with Target Business (the “Business Combination”) on or about [insert
date]. The Company shall notify you at least seventy-two ( 72) hours in advance of the actual date (or such shorter period as you may agree) of the consummation of the Business Combination (the
“Consummation Date”). Capitalized terms used but not defined herein shall have the meanings set forth in the Trust Agreement. 

In accordance with the terms of the Trust Agreement, we hereby authorize you to commence to liquidate all of the assets of the Trust Account
and to transfer the proceeds to a segregated account held by you on behalf of the Beneficiaries to the effect that, on the Consummation Date, all of the funds held in the Trust Account will be immediately available for transfer to the account or
accounts that the Company shall direct on the Consummation Date (including as directed to it by the Representatives on behalf of the Underwriters (with respect to the Deferred Discount)). 

On the Consummation Date (i) counsel for the Company shall deliver to you written notification that the Business Combination has been
consummated, or will be consummated concurrently with your transfer of funds to the accounts as directed by the Company (the “Notification”), and (ii) the Company shall deliver to you (a) a certificate by the Chief
Executive Officer, Chief Financial Officer, President or Chairman, which verifies that the Business Combination has been approved by a vote of the Company’s stockholders, if a vote is held and (b) a joint written instruction signed by the
Company and the Representatives with respect to the transfer of the funds held in the Trust Account, including payment of amounts owed to public stockholders who have properly exercised their redemption rights and payment of the Deferred Discount
directly to the account or accounts directed by the Representatives from the Trust Account (the “Instruction Letter”). You are hereby directed and authorized to transfer the funds held in the Trust Account immediately upon
your receipt of the Notification and the Instruction Letter, in accordance with the terms of the Instruction Letter. In the event that certain deposits held in the Trust Account may not be liquidated by the Consummation Date without penalty, you
will notify the Company in writing of the same and the Company shall direct you as to whether such funds should remain in the Trust Account and be distributed after the Consummation Date to the Company. Upon the distribution of all the funds, net of
any payments necessary for reasonable unreimbursed expenses related to liquidating the Trust Account, your obligations under the Trust Agreement shall be terminated. 












 In the event that the Business Combination is not consummated on the Consummation Date
described in the notice thereof and we have not notified you on or before the original Consummation Date of a new Consummation Date, then upon receipt by the Trustee of written instructions from the Company, the funds held in the Trust Account shall
be reinvested as provided in Section 1(c) of the Trust Agreement on the business day immediately following the Consummation Date as set forth in such notice as soon thereafter as possible. 












 
			
	Very truly yours,
	
	Hudson Executive Investment Corp. III
		
	By:	 	  

	Name:	 	
	Title	 	


  

			
	Agreed and acknowledged by:
		
	[•]	 	
		
	By:	 	  

		 	Name:
		 	Title:
		
	[•]	 	
		
	By:	 	  

		 	Name:
		 	Title:













 EXHIBIT B 

[Letterhead of Company] 

[Insert date] 
 Continental Stock
Transfer & Trust Company 1 State Street, 30th Floor New York, New York 10004 Attn: Francis Wolf & Celeste Gonzalez 
 Re:
Trust Account Termination Letter 
 Dear Mr. Wolf and Ms. Gonzalez: 

Pursuant to Section 1(i) of the Investment Management Trust Agreement between Hudson Executive Investment Corp. III
(the “Company”) and Continental Stock Transfer & Trust Company (the “Trustee”), dated as of ___________________ (the “Trust Agreement”), this is to advise you that the
Company has been unable to effect a business combination with a Target Business (the “Business Combination”) within the time frame specified in the Company’s Amended and Restated Certificate of Incorporation, as
described in the Company’s Prospectus relating to the Offering. Capitalized terms used but not defined herein shall have the meanings set forth in the Trust Agreement. 

In accordance with the terms of the Trust Agreement, we hereby authorize you to liquidate all of the assets in the Trust Operating Account and
to transfer the total proceeds into a segregated account held by you on behalf of the Beneficiaries to await distribution to the Public Stockholders. The Company has selected _________1 as the
effective date for the purpose of determining when the Public Stockholders will be entitled to receive their share of the liquidation proceeds. You agree to be the Paying Agent of record and, in your separate capacity as Paying Agent, agree to
distribute said funds directly to the Company’s Public Stockholders in accordance with the terms of the Trust Agreement and the Amended and Restated Certificate of Incorporation of the Company. Upon the distribution of all the funds, net of any
payments necessary for reasonable unreimbursed expenses related to liquidating the Trust Account, your obligations under the Trust Agreement shall be terminated, except to the extent otherwise provided in Section 1(i) of
the Trust Agreement. 
  

			
	Very truly yours,
	
	Hudson Executive Investment Corp. III
		
	By:	 	  

		 	Name:
		 	Title:


 cc: [•] and [•] 
  

	1 	 24 months from the closing of the Offering or such later date as may be approved by the Company’s
stockholders in accordance with the Company’s amended and restated certificate of incorporation. 














 EXHIBIT C 

[Letterhead of Company] 

[Insert date] 
 Continental Stock
Transfer & Trust Company 1 State Street, 30th Floor New York, New York 10004 Attn: Francis Wolf & Celeste Gonzalez 
 Re:
Trust Account Tax Payment Withdrawal Instruction 
 Dear Mr. Wolf and Ms. Gonzalez: 

Pursuant to Section 1(j) of the Investment Management Trust Agreement between Hudson Executive Investment Corp. III
(the “Company”) and Continental Stock Transfer & Trust Company (the “Trustee”), dated as of ___________________ (the “Trust Agreement”), the Company hereby requests
that you deliver to the Company $ of the interest income earned on the Property as of the date hereof. Capitalized terms used but not defined herein shall have the meanings set forth in the Trust Agreement. 

The Company needs such funds to pay for the tax obligations as set forth on the attached tax return or tax statement. In accordance with the
terms of the Trust Agreement, you are hereby directed and authorized to transfer (via wire transfer) such funds promptly upon your receipt of this letter to the Company’s operating account at: 

[WIRE INSTRUCTION INFORMATION] 
  

			
	Very truly yours,
	
	Hudson Executive Investment Corp. III
		
	By:	 	  

		 	Name:
		 	Title:


 cc: [•] and [•] 












 EXHIBIT D 

[Letterhead of Company] 

[Insert date] 
 Continental Stock
Transfer & Trust Company 1 State Street, 30th Floor New York, New York 10004 Attn: Francis Wolf & Celeste Gonzalez 
 Re:
Trust Account Stockholder Redemption Withdrawal Instruction 
 Dear Mr. Wolf and Gonzalez: 

Pursuant to Section 1(k) of the Investment Management Trust Agreement between Hudson Executive Investment Corp. III
(the “Company”) and Continental Stock Transfer & Trust Company (the “Trustee”), dated as of ____________________ (the “Trust Agreement”), the Company hereby requests
that you deliver to the redeeming Public Stockholders of the Company $ of the principal and interest income earned on the Property as of the date hereof to a segregated account held by you on behalf of the Beneficiaries. Capitalized terms used but
not defined herein shall have the meanings set forth in the Trust Agreement. 
 The Company needs such funds to pay its Public Stockholders
who have properly elected to have their shares of Common Stock redeemed by the Company in connection with a stockholder vote to approve an amendment to the Company’s amended and restated certificate of incorporation to modify the substance or
timing of the Company’s obligation to redeem 100% of public shares of Common Stock if the Company has not consummated an initial Business Combination within such time as is described in the Company’s amended and restated certificate of
incorporation or with respect to any other material provisions relating to stockholders’ rights or pre-initial Business Combination activity. As such, you are hereby directed and authorized to transfer
(via wire transfer) such funds promptly upon your receipt of this letter to a segregated account held by you on behalf of the Beneficiaries. 
  

			
	Very truly yours,
	
	Hudson Executive Investment Corp. III
		
	By:	 	  

		 	Name:
		 	Title:


 cc: [•] and [•]