Company: MYI
Filing Date: 2025-07-15
Form Type: 425
Source: 0001193125-25-159406
Chunk: 8

Company: BLACKROCK MUNIYIELD QUALITY FUND III, INC.
Filing Date: 2025-07-15
Form: 425
Chunk 8
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 remaining Shares the public holds. (See Section 9,             
 “Effects of the Offer; Consequences of Participation” and Section 17, “Fees and Expenses.”)                                                                                                                                                              |

iii

Does the Fund’s management recommend that stockholders participate in the Offer, and will management participate in the Offer?

| • |     | None of the Fund, the Board of Directors or the Investment Advisor is making any recommendation to stockholders                                                                                                                                        
 regarding whether to tender Shares for purchase or refrain from tendering Shares in the Offer. The Fund has been advised that none of its Board of Directors, officers or named portfolio managers intends to tender any Shares pursuant to the Offer. 
 (See Section 11, “Interests of Directors and Officers; Transactions and Arrangements Concerning the Shares.”)                                                                                                                                          |

Will there be additional opportunities to tender my Shares to the Fund?

| • |     | No other tender offers have been approved by the Board, but the Board reserves the right to approve tender offers 
 in the future. (See Section 2, “Purpose of the Offer” and Section 3, “Plans or Proposals of the Fund.”)           |

How do I obtain more information?

| • |     | Questions and requests for assistance may be directed to your financial advisor or other Nominee, or to the                                                                                        
 Information Agent toll free at (866) 961-8329. Requests for additional copies of this Offer to Purchase and the applicable Letter of Transmittal should also be directed to the Information Agent. |

The Information Agent for the Offer is: 51 West 52 ndStreet, 6 thFloor New York, NY 10019 (866) 961-8329(Toll Free) The Depositary for the Offer is:

| By First Class, Registered or Certified Mail: |     | By Express Mail or Overnight Courier: |
| Computershare Trust Company, N.A.             |     | Computershare Trust Company, N.A.     |
| Voluntary Corporate Actions                   |     | Voluntary Corporate Actions           |
| P.O. Box 43011                                
 Providence, RI 02940-3011                     |     | 150 Royall Street, Suite V            
 Canton, MA 02021                      |

iv

| 1. | Price; Number of Shares. |

Upon the terms and subject to the conditions of the Offer (including, if the Offer is extended or amended, the terms and conditions of any such extension or amendment), the Fund will accept for purchase