Exhibit 7.12

TCP-ASC ACHI SERIES LLLP

July 5, 2024

R1 RCM Inc.

434 W. Ascension Way, 6^th Floor

Murray, Utah 84123

Attn: General Counsel

Re: Waiver Request 

Ladies and Gentlemen:

Reference is hereby made to that certain Amended and Restated Investor Rights Agreement, dated as of June 21, 2022 (as amended, restated, supplemented or otherwise modified from time to time, the “Investor Rights Agreement”), by and among R1 RCM Inc., a Delaware corporation (the “Company”), R1 RCM Holdco Inc., a Delaware corporation, TCP-ASC ACHI Series LLLP, a Delaware limited liability limited partnership (the “Investor”) and, solely for purposes of Section 4, Section 6 and Section 11 thereof, certain Investor Affiliates. Capitalized terms used herein and not otherwise defined have the meanings ascribed to such terms in the Investor Rights Agreement.

The Investor hereby requests that the Company approve that the Investor, TowerBrook Capital Partners L.P., Ascension Health Alliance or any of their respective affiliates (collectively, the “TCP-ASC Parties”) may submit confidential private acquisition proposals to the Company with respect to the acquisition by the TCP-ASC Parties of all of the outstanding shares of common stock of the Company not currently owned by the TCP-ASC Parties, respond to any related inquiries from the Company and comply with any associated disclosure requirements resulting therefrom under applicable law. If the Company consents to the foregoing request, such consent shall extend to any subsequent proposals which may be made by the TCP-ASC Parties (or members of any group which may be formed of which they are a part), unless and until the Company withdraws such consent in writing.

We note in particular the obligations set forth in Section 6.2 of the Investor Rights Agreement that provide that “if the Board decides to engage in a process that could give rise to a change of control of the Company, the Company shall invite the Investor to participate in such process on the terms and conditions generally made available to the other participants in such process”.

For the avoidance of doubt, this request does not constitute a waiver of any provision of the Investor Rights Agreement except as expressly provided herein and each party to the Investor Rights Agreement expressly reserves all of its rights and remedies in respect of any breach thereof or other default thereunder. Section 11 of the Investor Rights Agreement shall apply to this letter, mutatis mutandis, as if expressly set out herein.

Sincerely yours,

TCP-ASC ACHI Series LLLP

By:	/s/ Glenn Miller
Name:	Glenn Miller
Title:	Vice President

Copies to:
Kirkland & Ellis LLP
300 North LaSalle
Chicago, Illinois 60654
Attention:	Richard W. Porter, P.C.
	Robert M. Hayward, P.C.
	Bradley C. Reed, P.C.
Email:	richard.porter@kirkland.com
	robert.hayward@kirkland.com
	bradley.reed@kirkland.com
Wachtell, Lipton, Rosen & Katz
51 West 52nd Street
New York, NY 10019
Attention:	Steven A. Cohen
	Victor Goldfeld
Email:	SACohen@wlrk.com
	VGoldfeld@wlrk.com