If an American woman marries a Caymanain Man that may have a record. Can they move to the state?

Would he be able to get citizenship?

Answer:
Would'nt think so.When you marry someone of a different nationality,You attain that persons nationality.Provided one of the partners is a citizen of the country you are married in.So you are now a legal citizen of Cayman Islands.However your spouse is'nt a citizen of the USA
why would the american women be marrying a man if she doesn't even know his criminal history?

you can be denied residency based on criminal history, yes.
I'm thinking with money, then Yes. Otherwise not.

The immigration information post by website user , MyTend.com not guarantee correctness

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