Financial Oversight and Management Board Integrity Act of 2023 This bill disqualifies certain third-party advisory or consulting firms with a potential conflict of interest from advising a Financial Oversight and Management Board. Such a board has been established for Puerto Rico. Specifically, a board must establish rules to disqualify any third-party advisory or consulting firm from advising the board for any period during which the firm has a client, or provides consulting services to, an individual, corporation, or other business entity that is competing for or performing a contract with the territorial government, the performance of which is within the board's jurisdiction.