Sending in a letter to Self Assessment office and reclaiming higher rate pension contributions

I need to send a letter to the SA office, to make an amendment to previous years returns and reclaim higher rate pension contributions for the last three/four years. Can I ask, 1. I believe I can claim back on the tax years, 2019-2020, 2020-2021, 2021-2022 ?? (is this right?). 2. Can I claim 2017-2018 and 2018-2019 tax years also? 3. Does my letter only need to arrive by the 5th April 2024 at the SA office. Are letters effectively date stamped - when they are received. Or does the letter/claims need to be processed by the SA office before the 5th April 2024 ?? The reason I ask, is that I checked the progress of the SA dept. online, which stated that the SA dept. are currently processing matters which arrived in mid-November 2023.

Hi David Raw,
The earliest year that you can make a claim for Personal Pension Relief is 2019-20.
This claim must be received by HMRC on or before 5 April 2024.
Although it may not be processed immediately, it must be received by then.
Please ensure that you enclose evidence of the contributions made each year and that is shows whether the contributions are gross or the net amount after tax relief.
Thank you.