Postal Service Financial Improvement Act of 201 9 This bill directs the Department of the Treasury to invest part of the Postal Service Retiree Health Benefits Fund in market-based index funds and establishes a Postal Service Retiree Health Benefits Fund Investment Committee to advise Treasury on investments made from the fund. Specifically, Treasury shall (1) invest a specified percentage of the fund, using one or more qualified professional asset managers, in index funds modeled after those established for Thrift Savings Fund investments; and (2) ensure that the investment replicates the performance of the longest-term target date asset allocation investment fund established by the Federal Retirement Thrift Investment Board. The specified percentage to be invested is defined as 25% of the currently available portions of the fund as are not immediately required for payments from the fund, except that the committee may specify a higher percentage, not to exceed 30%, not earlier than five years after this bill's enactment and as appropriate thereafter. Treasury shall annually engage an independent qualified public accountant to audit the financial statements of such investments and shall submit an annual management report that includes statements of financial position, operations, and cash flows; a statement on internal accounting and administrative control systems; the report resulting from the audit; and any other comments and information necessary to inform Congress about the operations and financial condition of the investments.