Stop the Spread of Invasive Mussels Act of 2019 This bill directs the Bureau of Reclamation to provide financial assistance to states with Reclamation projects to prevent the spread of aquatic invasive species into and out of reservoirs operated and maintained by Reclamation, including assistance to purchase, establish, operate, or maintain a watercraft inspection and decontamination station that has the highest likelihood of preventing the spread of aquatic invasive species. In providing financial assistance, Reclamation must prioritize projects that (1) prevent the spread of an aquatic invasive species to waters under its jurisdiction, including irrigation, reclamation, or other water projects; and (2) align with the priorities of the state and with the document titled Quagga-Zebra Mussel Action Plan for Western U.S. Waters , published in February 2010. The bill provides authority for each federal agency on the Aquatic Nuisance Species Task Force to (1) conduct mandatory inspections and decontamination of watercraft; and (2) if necessary, impound, quarantine, or otherwise prevent entry of a watercraft. The membership of the task force is expanded to include the National Park Service, Bureau of Land Management, and Reclamation.