Public Water Supply Invasive Species Compliance Act of 2019 This bill exempts certain water transfers between public water supplies in Texas, Arkansas, and Louisiana from prohibitions on illegal trade of plants and wildlife. Specifically, the prohibitions do not apply to covered water transfers containing a prohibited species if (1) the species are present in both public water supplies before the transfer and the water is transferred directly between them; or (2) the water is transferred in a closed conveyance system, such as a pipe system, and sent directly to treatment facilities where the species will be destroyed.