Further Continuing Appropriations Act, 2020, and Further Health Extenders Act of 2019 This bill provides continuing FY2020 appropriations to federal agencies through December 20, 2019, and extends several expiring health programs. It is known as a continuing resolution (CR) and prevents a government shutdown that would otherwise occur if the FY2020 appropriations bills have not been enacted when the existing CR expires after November 21, 2019. The CR funds most programs and activities at the FY2019 levels with several exceptions that provide funding flexibility and additional appropriations to various programs, including the 2020 Census, the Indian Health Service, Ebola preparedness and response activities, the Commodity Supplemental Food Program, and the Payment in Lieu of Taxes program. The bill temporarily extends several authorities and programs, including several public health, Medicare, and Medicaid authorities and programs; the Temporary Assistance for Needy Families (TANF) program and related programs; certain provisions of the Foreign Intelligence Surveillance Act; the National Flood Insurance Program; several authorities related to immigration; the Calfed Bay-Delta Authorization Act; the National Advisory Committee on Institutional Quality and Integrity; the Export-Import Bank of the United States; and the U.S. Commission on International Religious Freedom. The bill also provides a pay raise for the military, repeals a rescission of state highway funding, and modifies the U.S. Victims of State Sponsored Terrorism Fund.