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They can file joint for 2021 but that means he is electing to pay US tax on his worldwide income for 2021.

Like Susan says, it is possible to file jointly but that's an election under §6013, not the garden variety check-the-box deal you have on F.1040, and there are implications for making that election, beyond being subject to US tax on worldwide income from Jan 1, 2021.

At this point, you're no longer talking about EIP3.  You're referring to 2021 RRC.  The husband's eligibility will be predicated on whether he was at least a dual-status resident alien since the SSN was already issued in Jan 2022 before the filing due date.  For that, you'd look to substantial presence test, failing which, first-year or joint filing election could make him a resident alien.

Before pulling the trigger, you should review the husband's finances, especially overseas accounts, retirement arrangements, and assets/investments more thoroughly, how the election(s) could impact the couple's tax liabilities, information return filing requirements, and the downstream implications, and have a discussion with the couple so that they can make an informed decision with a clear understanding of what they're signing up for.

If the couple's finances are straightforward, that should be easy enough.  But if your clients are mid-career or senior executives from overseas, they tend to have more sophisticated finances (including foreign pensions, mutual funds investments) that could complicate things from a US tax perspective.