According to U.S. immigration law, the second marriage will not be recognized at all. The person would need to get an official, legal divorce from his first wife. Then, once that divorce has become final, the person would need to legally marry the woman who wants to immigrate to the United States.
I suggest that you consult with an immigration attorney about the case.
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I agree with Mr. Carlin, the second marriage will not be recognized because the first marriage was not terminated prior to the second marriage taking place.
This is general information and not legal advise. This communication does not create a lawyer-client relationship.