Military Service Academy Foundation Support Act of 2022 This bill authorizes the military departments to provide specified support, with limitations, to charitable, educational, or civic nonprofit organizations that operate exclusively to support the service academies (i.e., the U.S. Military Academy, U.S. Naval Academy, and U.S. Air Force Academy). Specifically, the bill authorizes the military departments to provide (1) the use of facilities or equipment of the United States on an unreimbursed basis, and (2) endorsement from specified individuals related to an organization and its events and activities.