Firearms Fairness and Security Act - Amends the Federal criminal code to prohibit the sale or other disposition of a firearm or ammunition to, or the possession or shipment of a firearm or ammunition by, a person who has been indicted or convicted in any court outside the United States of a crime punishable by imprisonment exceeding one year (except for an antitrust law violation) if such crime would be punishable by imprisonment exceeding one year in the United States.