Puerto Rico Health Care Fairness, Accountability, and Beneficiary Access Act of 2019 This bill alters certain funding and payment mechanisms, and establishes several requirements, for Puerto Rico's Medicaid program. Among other changes, the bill increases the Federal Medical Assistance Percentage (FMAP) from 55% to 83% through FY2029; beginning in FY2030, the FMAP must be calculated in the same manner as for states (i.e., based on per capita income). Puerto Rico must also expand its Medicaid program to include certain items, services, and populations that states are already required to cover; failure to do so results in a reduction of the applicable FMAP. Additionally, beginning in FY2025, the bill excludes Puerto Rico from a Medicaid funding cap that currently applies to U.S. territories.