Is it permissible to marry an American woman "on paper only" to obtain American citizenship for a better future, and would the first wife agree to that?

It is permissible to marry an American woman if she is a Muslim or a chaste woman of the People of the Book. It is not permissible if she is a polytheist or an atheist. Marriage is either valid, fulfilling its conditions and pillars such as the consent of both parties, the dowry, two witnesses, and the woman's guardian, in which case its legal effects are established; or it is invalid if it does not fulfill them. There is no such thing in Islamic law as marriage "on paper only." If a man marries another woman in a legally valid marriage that fulfills the conditions and has no specified duration, it is polygyny, and the first wife has no right to object. However, if the marriage does not fulfill the conditions or is a temporary marriage to obtain citizenship, then it is invalid, and she has the right to object to it.