Supporting Activities & Leadership Abroad to Move Amphibians Nearing Decline or Extinction to Recovery Act of 2019 or the SALAMANDER Act of 2019 This bill establishes a Highly Endangered Amphibian Species Conservation Fund and requires the Department of the Interior to use the fund to carry out a grant program for the conservation of highly endangered amphibian species. Highly endangered amphibian species means any amphibian species categorized on the International Union for Conservation of Nature (IUCN) Red List of Threatened Species as either endangered or critically endangered. The term also means any other amphibian species categorized on such list as data deficient or under a threat category lower than endangered if Interior determines that (1) the most recent IUCN Red List assessment indicates that the population is decreasing, or (2) such species is facing new or emerging threats. The bill establishes the fund as a separate account in the Multinational Species Conservation Fund.