Fairness for American Victims of State-Sponsored Terrorism Act This bill authorizes and provides funding for additional payments from the U.S. Victims of State Sponsored Terrorism Fund. Specifically, the bill (1) provides lump-sum catch-up payments from the fund to 9/11 victims and their families; and (2) makes victims of the 1983 bombing of the U.S. Marine Corps barracks in Beirut and their families eligible for lump-sum catch-up payments from the fund. The bill also rescinds specified unobligated funds that were provided for (1) the Small Business Administration's Paycheck Protection Program, and (2) emergency rental assistance.