When did the check arrive in the mail box, when was the envelope canceled, and can you prove it?
There is an easy answer and a hard answer.
The easy answer is, file an amended return and report the W-2.
The hard answer is: the IRS follows the doctrine of constructive receipt. If you did not receive the money in spendable condition until 2022, then it is 2022 income. However, if you leave the W-2 off your 2021 tax return and don't amend, you can expect to get a letter from the IRS. You would have to reply by explaining the situation, citing the doctrine of constructive receipt, and that even though the check was dated 12/30, the envelope wasn't canceled until 1/3 and you received it on 1/5 (or whatever); and letting the IRS know you plan to report the income in 2022. They might or might not accept your argument.
(It becomes more complicated to win that argument if you knew before 12/30 that you had won the settlement and were just waiting for a check you knew was coming.)
