<PAGE>


                                                                    EXHIBIT 10.5

                            STOCK PURCHASE AGREEMENT
                            -----------------------

     THIS STOCK PURCHASE AGREEMENT (the "Agreement") is made and entered into as
of December 13, 2001 by and between j2 GLOBAL COMMUNICATIONS, INC., a Delaware
corporation, on the one hand ("Company"); and each of the following entities, on
the other hand: FISHER CAPITAL LTD., a Cayman Island company ("Fisher"), and
WINGATE CAPITAL LTD., a Cayman Island company ("Wingate", and together with the
Fisher, the "Shareholders").

                                   Background
                                   ----------

     A. Each Shareholder owns the number of shares of Common Stock, $0.01 par
value per share ("Common Stock"), of the Company set forth opposite such
Shareholder's name beneath the column entitled "Common Shares" on the attached
Schedule A (collectively, the "Shares"), each Shareholder owns Penny Warrants
----------
(defined below) to purchase the number of shares of Common Stock set forth
opposite such Shareholder's name beneath the column entitled "Penny Warrants" on
Schedule A, and each Shareholder owns Other Warrants (defined below) to purchase
----------
the number of shares of Common Stock set forth opposite such Shareholder's name
beneath the column entitled "Other Warrants" on Schedule A (the "Other
                                                ----------
Warrants", and collectively with the Penny Warrants and the Shares, the
"Securities").

     B. For purposes of this Agreement, the term "Penny Warrants" refers to the
warrants to purchase shares of Common Stock having an exercise price of $0.04
per share, as adjusted to date, issued pursuant to the Agreement and Plan of
Merger (the "Merger Agreement"), dated as of July 13, 2000, among Company,
eFax.com, a Delaware corporation, and JFAX.COM Merger Sub, Inc., a Delaware
corporation, and in accordance with the Side Agreement (as defined in the Merger
Agreement).

     C. For purposes of this Agreement, the term "Other Warrants" refers to the
warrants to purchase shares of Common Stock having an exercise price of $209.76
per share, as adjusted to date, issued pursuant to the Merger Agreement and in
accordance with the Side Agreement (as defined in the Merger Agreement).

     D. Each Shareholder desires that the Company purchase all of the Securities
owned of record or beneficially by such Shareholder, and the Company is willing
to purchase such Securities, all on the terms and subject to the conditions set
forth in this Agreement.

                                    Agreement
                                    ---------

NOW, THEREFORE, in consideration of the premises and of the undertakings of the
parties hereinafter set forth, the Shareholders and the Company agree as
follows:

                                    ARTICLE I

                                    PURCHASE
                                    --------

   1.1 Agreement of Purchase. On the date hereof, subject to the terms and
   -------------------------
conditions of this Agreement, the Company shall purchase from each Shareholder,
and each Shareholder shall sell to the Company, the Securities owned by such
Shareholder (as set out on Schedule A).
                           ----------

   1.2 Purchase Price. The purchase price for each Share shall be $4.00. The
   ------------------
purchase price for each Penny Warrant shall be the product of (I) $4.00,
multiplied by (II) the number of shares of Common Stock subject to such Penny
Warrant as set forth on Schedule A (with respect to each Penny Warrant, the
                        ----------
"Penny Warrant



<PAGE>

Purchase Price"). The purchase price for each Other Warrant shall be the product
of (I) $0.01, multiplied by (II) the number of shares of Common Stock subject to
such Other Warrant as set forth on Schedule A (with respect to each Other
                                   -----------
Warrant, the "Other Warrant Purchase Price"). In full consideration of the
receipt by the Company of (a) the Shares set forth opposite each Shareholder's
name on Schedule A, which Shares shall be delivered to the Company through DTC,
        ----------
and (b) the original instrument evidencing the Penny Warrants and Other Warrants
set forth each Shareholder's name on Schedule A, the Company will pay to each
                                     ----------
Shareholder a sum equal to: (i) $4.00 multiplied by the number of Shares set
forth opposite such Shareholder's name on Schedule A (which dollar amount is set
                                          ----------
forth opposite such Shareholder's name under the column entitled "Share Purchase
Price" on Schedule A), plus (ii) the Penny Warrant Purchase Price for such
          ----------
Shareholder's Penny Warrant (which dollar amount is set forth opposite such
Shareholder's name under the column entitled "Penny Warrant Purchase Price" on
Schedule A), plus (ii) the Other Warrant Purchase Price for such Shareholder's
----------
Other Warrant (which dollar amount is set forth opposite such Shareholder's name
under the column entitled "Other Warrant Purchase Price" on Schedule A)
                                                            ----------
(collectively, with respect to each Shareholder, the "Purchase Price"). The
total Purchase Price payable to each Shareholder is set forth opposite such
Shareholder's name beneath the column "Total Purchase Price" on Schedule A. Each
                                                                ----------
Shareholder's Purchase Price shall be payable on the date hereof by wire
transfer of immediately available funds to an account specified in writing by
such Shareholder. Each Shareholder agrees to cause to be transferred to Company
the number of Shares, the Penny Warrant and Other Warrant purchased by the
Company from such Shareholder as set forth in this Section 1.2.

   1.3 Sales and Transfer Taxes.  All applicable sales, transfer, stamp, and
       ------------------------
documentary taxes, if any, which may be due or payable as a result of the
transactions contemplated hereby shall be borne and paid by the Company.

                                   ARTICLE II

                         REPRESENTATIONS AND WARRANTIES
                         ------------------------------

   2.1 Representations and Warranties of each Shareholder. To induce the Company
       --------------------------------------------------
to purchase the Securities, each Shareholder hereby represent and warrant to the
Company as follows:

        2.1.1 Authority of each Shareholder. Such Shareholder has full power and
              -----------------------------
authority to execute and deliver this Agreement, to perform each and all of such
Shareholder's obligations under and pursuant hereto and to consummate the
transactions contemplated herein.

        2.1.2 This Agreement. This Agreement has been duly executed and
              --------------
delivered by such Shareholder and is the legal, valid, and binding obligation of
such Shareholder enforceable against such Shareholder in accordance with its
terms.

        2.1.3 No Conflicts. The execution, delivery and performance of this
              ------------
Agreement by such Shareholder and the consummation by it of the transactions
contemplated herein do not and will not (i) result in a violation of such
Shareholder's Certificate of Incorporation or By-laws (or other similar
governing documents), (ii) conflict with, or result in the breach or
termination of any provision of, or constitute a default or violation under (in
each case whether with or without giving notice or the lapse of time or both)
of any indenture, mortgage, lease, deed of trust, or other instrument, contract
or agreement to which such Shareholder is a party or bound, or (iii) result in
a violation of any law, rule, regulation, judgment, order, arbitration award or
decree to which such Shareholder is bound or any of its properties are bound.

        2.1.4 No Approvals. No approval, authority or consent of, or filing by
              ------------
such Shareholder with, or notification to, any foreign, federal, state or local
court, authority or governmental or regulatory body or agency or individual,
corporation, partnership, limited liability company, or other entity of any kind
whatsoever is necessary in connection with such Shareholder's execution,
delivery or performance of this Agreement or the consummation by the Shareholder
of the transactions contemplated hereby.



<PAGE>


        2.1.5 Title to Securities. Assuming that such Shareholder received the
              -------------------
Securities from the Company free, clear and discharged of any and all pledges,
security interests, liens, adverse claims, obligations, options, charges, trusts
and other encumbrances or interests of a third party whatsoever, then such
Shareholder holds the Securities free, clear and discharged of any and all
pledges, security interests, liens, adverse claims, obligations, options,
charges, trusts or other encumbrances or interests of a third person whatsoever.
Such Shareholder owns the Securities set forth opposite such Shareholder's name
on the attached Schedule A.
                ----------

        2.1.6 Investigation. Such Shareholder has made such investigation as it
              -------------
has deemed appropriate in connection with the decision to enter into this
Agreement. The Company has provided such Shareholder with all such information,
financial and otherwise, as such Shareholder has requested in connection with
such investigation. Such Shareholder is relying on the results of such
investigation and the advice of its personal advisors and has not relied upon
or been influenced by any statement or representation made by the Company or
any director, officer, employee, agent or affiliate thereof, other than the
covenants of the Company under this Agreement and the representations and
warranties of the Company set forth herein. Such Shareholder has been advised to
seek the advice of an attorney and its financial and tax advisor(s) in
connection with the transaction contemplated in this Agreement.

        2.1.7 Purchase Price and Other Terms and Conditions. Such Shareholder
              ---------------------------------------------
hereby acknowledges that, in extending and negotiating the purchase of the
Securities for the Purchase Price and upon and subject to the other terms and
conditions set forth in this Agreement, the Purchase Price and those other
terms and conditions have been represented to such Shareholder purely as those
upon which the Company has been willing to go forward with said purchase, and
that no statement or representation whatsoever has been made to such
Shareholder or to any other person or entity, by the Company or any director,
officer, employee, agent or affiliate of the Company concerning the fairness of
the Purchase Price.

        2.1.8 Future Actions. Such Shareholder understands and further
              --------------
acknowledges that, at any time or from time to time after the date of the
execution of this Agreement, the Company may formulate plans or intentions or
may take or cause to be taken various actions (including, by way of example
rather than by way of limitation, negotiation with other Company shareholders
with a view to purchasing shares of the Company's stock owned by such
shareholders, entrance into merger, acquisition, share exchange or asset
disposition negotiations or agreements, and registration and listing of shares
of Company stock for public trading) which ultimately may result in receipt by
some or all other Company shareholders of substantially greater consideration
for their shares of capital stock of the Company on substantially more
favorable terms and conditions than afforded the Shareholders under this
Agreement, and such Shareholder hereby additionally acknowledges that no
statement or representation whatsoever (other than the representations and
warranties of the Company set forth herein) has been made to such Shareholder
by the Company or any director, officer, employee, agent or affiliate of the
Company concerning what, if any, present intentions or understanding the
Company or any such person may have, or what, if any, proposals or offers the
Company or any such person may have made or received, with respect to any such
actions.

        2.2 Representations and Warranties of Company. To induce the
            -----------------------------------------
Shareholders to sell the Securities to the Company, the Company hereby
represents and warrants to each Shareholder as follows:

            2.2.1  Organization and Good Standing.  The Company is a
                   ------------------------------
corporation organized and existing in good standing under the laws of the State
of Delaware.

            2.2.2 Authority of the Company. The Company has all requisite
                  ------------------------
corporate power to execute and deliver this Agreement and to engage in, and
consummate, the transactions contemplated by this Agreement. The execution,
delivery and performance of this Agreement by the Company have been authorized
by all necessary corporate action on the part of the Company.

            2.2.3 No Approvals.  No approval, authority or consent of, or
                  ------------
filing by the Company with, or notification to, any foreign, federal, state or
local court, authority or governmental or regulatory body or agency


<PAGE>


or individual, corporation, partnership, limited liability company, or other
entity of any kind whatsoever is necessary in connection with the execution,
delivery or performance of this Agreement, or the consummation of the
transactions contemplated hereby.

            2.2.4 This Agreement. This Agreement has been duly executed and
                  --------------
delivered by the Company and is legal, valid, and binding obligations of the
Company enforceable against the Company in accordance with its terms.

            2.2.5. No Conflicts. The execution, delivery and performance of this
                  ------------
Agreement by the Company and the consummation by it of the transactions
contemplated herein do not and will not (i) result in a violation of the
Company's Certificate of Incorporation or By-laws, (ii) conflict with, or result
in the breach or termination of any provision of, or constitute a default or
violation under (in each case whether with or without giving notice or the lapse
of time or both) any indenture, mortgage, lease, deed of trust, or other
instrument, contract or agreement to which the Company is a party or bound or
(iii) result in a violation of any law, rule, regulation, judgment, order,
arbitration award or decree to which the Company is a party or by which it is
bound or any of its properties are bound.

                                   ARTICLE III

                                  MISCELLANEOUS
                                  -------------

             3.1 Survival of Representations and Warranties; Indemnification.
                 ------------------------------------------------------------
The representations and warranties contained herein shall survive the
consummation of the transactions contemplated hereby. From and after the date
hereof, the Shareholders, individually and not jointly and severally, shall
indemnify, defend, and hold harmless the Company and each officer, director,
agent, employee and affiliate thereof (collectively, "Company Indemnitees") from
and against any and all damages incurred by any of the Company Indemnities in
connection with, arising from, or as a result of any breach by any Shareholder
of any agreement, covenant, or representation or warranty set forth in this
Agreement. From and after the date hereof, the Company shall indemnify, defend,
and hold harmless each Shareholder and each officer, director, agent, employee
and affiliate thereof (collectively, "Shareholder Indemnitees") from and against
any and all damages incurred by any Shareholder Indemnitee in connection with,
arising from, or as a result of any breach by the Company of any agreement,
covenant, or representation or warranty set forth in this Agreement.

            3.2 Entire Agreement, Waivers, and Amendment. This Agreement
                ----------------------------------------
constitutes the entire agreement of the parties related to the Company's
purchase from the Shareholders and either Shareholder's sale to the Company of
the Securities and supersedes all prior and contemporaneous agreements,
understandings, negotiations, and discussions, whether oral or written, of the
parties regarding the Company's purchase from the Shareholders and either
Shareholder's sale to the Company of the Securities, and there are no other
agreements between the parties regarding the Company's purchase from the
Shareholders and either Shareholder's sale to the Company of the Securities
except as set forth specifically herein. No amendment, supplement, modification,
or waiver of this Agreement shall be implied or be binding unless in writing and
signed by all of the parties hereto. No waiver of any provisions of this
Agreement shall be deemed or shall constitute a waiver of any other provision
hereof (whether or not similar), nor shall such waiver constitute a continuing
waiver, unless otherwise expressly therein provided.

            3.3 No Brokerage. Each party to this Agreement represents and
                ------------
warrants that no broker, agent, or finder has been retained or is entitled to be
paid by such party in connection with the transactions contemplated by this
Agreement and that no brokerage or finder's or agent's fee or other commission
has been agreed to be paid by such party for or on account of this Agreement.

            3.4 Successors and Assigns. All of the terms and provisions of this
                ----------------------
Agreement by or for the benefit of the parties shall be binding upon and inure
to the benefit of their successors, assigns, heirs, and personal
representatives. The rights and obligations provided by this Agreement shall not
be assignable by any party

<PAGE>


without the written consent of the other parties, and except as expressly
provided herein nothing herein is intended to confer upon any person other than
the parties and their successors any rights under or by reason of this
Agreement.

     3.5. Counterparts. This Agreement may be executed in two or more
          ------------
counterparts, each of which shall be deemed an original, but all of which
together shall constitute one and the same instrument.

     3.6 Headings. The Article and Section heading contained in this Agreement
         --------
are for reference purposes only and shall not affect in any way the meaning or
interpretation of this agreement.

     3.7 Severability. If any term or provision of this Agreement, or the
         ------------
application thereof to any circumstances shall, to any extent and for any
reason, be held invalid or unenforceable, the remainder of this Agreement, or
the application of such term or provisions to circumstances other than those to
which it is held to be invalid, or unenforceable, shall not be affected thereby
and shall be construed as if such invalid or unenforceable term or provision had
never been contained herein, and each term and provisions of this Agreement
shall be valid and enforceable tot he fullest extent permitted by law.

     3.8 Governing Law and Choice of Forum. This Agreement shall be governed by
         ---------------------------------
and construed under and pursuant to the internal laws of the State of California
(other than principles of conflicts of laws). Any and all actions concerning any
dispute arising under this Agreement may be filed and maintained in a state or
federal court sitting in Los Angeles County, California or any other court
having jurisdiction over such action or dispute.

     3.9. Expenses. Each of the parties hereto shall pay all expenses (including
          --------
attorneys' fees) incurred by such party in connection with the entry into this
Agreement and the consummation of the transactions contemplated hereby.

             [The balance of this page is intentionally left blank.]

<PAGE>


     IN WITNESS WHEREOF, the Company and the Shareholders have executed this
Agreement as of the day and year first above written.

                                    "Company"

                                    j2 GLOBAL COMMUNICATIONS, INC.

                                    By  /s/ Scott M. Jarus
                                        ----------------------------
                                        Scott M. Jarus

                                    Its President

                                    "Shareholders"

                                    FISHER CAPITAL LTD.

                                    By:  /s/ Daniel J. Hopkins
                                        ---------------------------
                                         Daniel J. Hopkins

                                    Its: Authorized Signatory
                                        ---------------------------

                                    WINGATE CAPITAL LTD.

                                    By:  /s/ Daniel J. Hopkins
                                        ---------------------------
                                    Its: Authorized Signatory
                                        ---------------------------

<PAGE>

<TABLE>
<CAPTION>


                                   Schedule A

                                        Shares                  Penny Warrant              Other Warrant       Total
                                       Purchase       Penny       Purchase       Other       Purchase         Purchase
Shareholder               Shares        Price        Warrants       Price       Warrants       Price           Price
-----------               ------        -----        --------       -----       --------       ------          -----
<S>                        <C>           <C>            <C>           <C>         <C>          <C>              <C>
FISHER CAPITAL LTD.       257,721    $1,030,884       426,724     $1,706,896     12,968        $129.68      $2,737,909.68

WINGATE CAPITAL LTD.      139,503     $558,012        229,526     $  918,104      6,983        $ 69.83      $1,476,185.83

Totals:                   397,224    $1,588,896       656,250     $2,625,000     19,951        $199.51      $4,214,095.51

</TABLE>