Presidential Tax Filings and Audit Transparency Act of 2022 This bill requires the Internal Revenue Service (IRS) to conduct an examination to determine the correctness of a Presidential income tax return as rapidly as practicable after it is filed. The IRS must disclose and make publicly available (on the internet) an initial report, periodic reports, and a final report on the examination of such tax returns. The final report must include the date on which the IRS examination of the return was completed, a list of audit materials, and a description of each proposed adjustment to a return and any controversy relating to its examination. This disclosure of tax return information is an exception to the general rule of confidentiality of taxpayer returns. The bill provides criteria for approving a request for an extension of the filing of a tax return and for failing to file a return within the required time period. The bill defines Presidential income tax return as any relevant income tax return of (1) a president while the president is in office, (2) the spouse of a president, (3) a corporation or partnership controlled by a president or a president's spouse, and (4) the estate of a president or a president's spouse.