No, there is no immigration form required to get married in the US. As I said above, he either needs a valid green card, valid visa, or the ESTA to enter the US... once he's in the US, he can get married.
I don't know what would happen if his green card didn't work, though. I'm not sure if they would let him in as a visitor or if he would get sent back to the UK without being allowed in.
How long has it been since he moved back to the UK? If he's been gone more than 6 months, in order to be allowed back into the US on the green card he would have to prove he is still a US resident (I.e. he rents/owns in the US, works in the US, pays US taxes, has a US driver's licence etc.) and that he spends more time per year in the US than in the UK. He may even need to apply for a re-entry permit or a returning resident card before coming back.
See here:
http://lawandborder.com/risk-abandoning-green-card-abroad-6-months/Honestly, it sounds like it could be easier for you to apply for a fiancé visa and marry in the U.K., rather than risk him having issues getting into the US with his green card.
Actually, aren't you applying for a fiancé visa anyway? All of your previous posts are about preparing your fiancé visa application.
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