Territories Medicare Prescription Drug Assistance Equity Act of 2019 This bill makes certain subsidies under the Medicare prescription drug benefit available to beneficiaries who reside in Puerto Rico or another U.S. territory. Current law makes such beneficiaries ineligible for premium and cost-sharing subsidies, but establishes a process for U.S. territories to apply for financial assistance with respect to the provision of Medicare prescription drugs. The bill eliminates this process and makes the subsidies available to beneficiaries who reside in a U.S. territory and are otherwise eligible.