Putting Investors First Act of 2022 This bill requires a proxy advisory firm to register with the Securities and Exchange Commission and prohibits an unregistered proxy advisory firm from using interstate commerce to provide proxy-voting advice, research, analysis, or recommendations to any client. With respect to these firms, the bill (1) establishes procedures for both registration and termination of registration; (2) requires each firm to employ an ombudsman, designate a compliance officer, and publicly disclose conflicts of interest; (3) allows issuers to assess and comment on proxy voting recommendations; and (4) prohibits unfair, coercive, or abusive practices. The bill establishes a private right of action against a proxy advisory firm that endorses an approved proposal that is not supported by the issuer and is found to be illegal.