Make Border Security a Priority Act of 2022 This bill requires the Department of Homeland Security (DHS) to, for FY2022 and FY2023, expend on enhancing security along the U.S.-Mexico border an amount that is equal to the amount appropriated to the Department of Defense for the Ukraine Security Assistance Initiative for that fiscal year. The bill also authorizes the President to liquidate property seized from sanctioned Russian individuals and entities. The resulting funds shall be available without further appropriation to DHS for physical infrastructure and equipment to enhance security along the U.S.-Mexico border.