Company: MYI
Filing Date: 2025-07-15
Form Type: 425
Source: 0001193125-25-159406
Chunk: 6

Company: BLACKROCK MUNIYIELD QUALITY FUND III, INC.
Filing Date: 2025-07-15
Form: 425
Chunk 6
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 to the date and time the Offer expires,                                                                                                                                          
 complete and execute a Letter of Transmittal, together with any required signature guarantees, and any other documents required by the Letter of Transmittal. You must send these materials to the Depositary at its address set forth on the last page 
 of this offer. If you hold certificates for Shares, you must send the certificates to the Depositary at its address set forth on the last page of this offer. If your Shares are held in book-entry form, you must comply with the book-entry delivery  
 procedure set forth in Section 5.C of this Offer. In all these cases, the Depositary must receive these materials prior to the date and time the Offer expires. If any certificate representing Shares has been mutilated, lost, stolen or              
 destroyed, the stockholder should promptly call the Depositary at (781) 575-2879 or (800) 699-1236. The stockholder will then be instructed by the Depositary                                                                                           
 as to the steps that must be taken to replace the certificate. The Letter of Transmittal and related documents cannot be processed until the procedures for replacing lost or destroyed certificates have been followed.                                |

ii

Must I tender all of my Shares for purchase?

| • |     | No. You may tender for purchase all or part of the Shares you own. (See Section 1, “Price; 
 Number of Shares.”)                                                                        |

May I withdraw my Shares after I have tendered them for purchase and, if so, by when?

How do I withdraw previously tendered Shares?

| • |     | You must submit or direct your Nominee to submit a request for withdrawal of previously tendered Shares to the                                                                             
 Depositary. You may withdraw only all Shares previously tendered by you, and not a portion thereof, and your request for withdrawal must state this. (See Section 6, “Withdrawal Rights.”) |

May my Nominee place any conditions on my tender of Shares?

| • |     | No. |

May I place any conditions on my tender of Shares?

| • |     | No. |

Is my tender of Shares in the Offer a taxable transaction?

| • |     | It is anticipated that the tender of Shares in exchange for cash will generally be a taxable transaction for U.S.                                                                                                                  
 federal income tax purposes either in the form of a “sale or exchange” or, under certain circumstances, a “dividend.” Please consult your tax adviser regarding your individual tax