Praise be to Allah.and peace be upon the Messenger of Allaah.
We put this question to Shaykh al-‘Allaamah ‘Abd al-‘Azeez ibn Baaz, who responded: “It is not one of the purposes of marriage according to Islamic sharee’ah to marry for the purpose of gaining residency rights and then to get divorced. It seems to me that this is not permitted.”
Moreover, marrying a Christian woman on paper only is a kind of cheating these kaafirs, and this is not permitted. Allaah does not approve of wrongdoing even to kaafirs. And Allaah knows best.