Marine Mammal Research and Response Act of 2019 This bill reauthorizes through FY2025 and generally revises the John H. Prescott Marine Mammal Rescue Assistance Grant Program, including by renaming the program as the John H. Prescott Marine Mammal Rescue and Response Grant Program. The bill also establishes the John H. Prescott Marine Mammal Rescue and Rapid Response Fund for providing emergency financial assistance for certain stranded or entangled marine mammals and otherwise provides support for marine mammals.