Post Office Security and Transparency Act of 2020 or the POST Act This bill requires the U.S. Postal Service (USPS) to take specified actions to ensure the availability of mail collection boxes. Specifically, the bill (1) prohibits the USPS from removing any collection box during the period beginning on this bill's enactment and ending on the later of 180 days after enactment or the date on which the USPS submits a report to Congress providing details of collection box removals and relocations, and (2) requires the USPS to restore or replace any collection box that it removed during the period beginning on June 16, 2020, and ending on the day before this bill's enactment.