I'm just going to fill out my 2022 tax return with the contribution and be done with it. The IRS got more money than the should have in 2021 this just corrects it.
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probably won't work. the HSA custodian reports to the IRS what you denoted as 2022 contributions while you'll be reporting more. expect a notice from them if you do this.
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you may even eventually get a notice from the IRS for 2021 because the HSA custodian reported more than you.
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these notices may never show up or could take a year or two
i would say the best thing to do would be to amend 2021.
then if you want you can transfer any funds from the current HSA a/c to a new one that allows corrections in situations like yours.
