No, you cannot file an amendment for 2020 to add the unemployment compensation you received in 2022 even though you should have received it in 2020. The IRS states that “The American Rescue Plan provides unemployment compensation exclusion relief only for unemployment compensation received in 2020". The exclusion does not apply to unemployment compensation that was received in 2022. You must report the unemployment compensation in the year that you received it.
Please review the IRS Fact Sheet 2020 Unemployment Compensation Exclusion FAQs. Question 6 applies to your situation.
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