Federally Integrated Species Health Act or the FISH Act This bill amends the Endangered Species Act of 1973 to transfer the responsibility for administering the Act from the Commerce Department's National Marine Fisheries Service (NMFS) to the Department of the Interior's U.S. Fish and Wildlife Service (USFWS) with respect to anadromous species (species of fish that spawn in fresh or estuarine waters and that migrate to ocean waters) and catadromous species (species of fish that spawn in ocean waters and migrate to fresh waters). Under current law, the Act is administered by both the NMFS and the USFWS.