Supporting Victims of Iranian Terrorism Act of 2019 This bill authorizes jurisdiction over certain Iranian assets so that judgments against Iran for the 1983 bombing of the U.S. Marine barracks in Beirut, Lebanon, may be collected by the victims' families. Specifically, the bill establishes personal jurisdiction for the U.S. District Court for the Southern District of New York over Iranian funds held outside the United States by any foreign securities intermediary.