What is the statue of limitation for outstanding warrant for benefits fraud?

My husband before he moved to the US was receiving housing, disabilty, and living allowance benefits. When he moved to the US a yr ago, he cont. to draw benefits for 9 months till he got his green card. We recently have found out he has an outstanding warrant for benefits fraud. We didnt even know he committed fraud. He maintained his flat in UK until he was sure he could stay in the US. What are the statue of limitation for an outstanding warrant for fraud? And should he return to UK using and American pport will he be arrested at the airport? How can we clear this up without him having to return to UK? Can we try to repay the monies he shouldnt have taken?