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Wiktionary
sham marriage

n. A marriage of convenience entered into purely for the purpose of gaining a benefit or other advantage arising from that status, usually with the intent of deceiving public officials or society about its purpose.

Wikipedia
Sham marriage

A sham marriage or fake marriage is a marriage of convenience entered into purely for the purpose of gaining a benefit or other advantage arising from that status. While referred to as a "sham" or "fake" because of its motivation, the union itself is still legally valid if it conforms to the formal legal requirements for marriage in that country. Arranging or entering into such a marriage to deceive public officials is itself a separate violation of the law of some countries. In the United States, sham marriage for purposes of immigration fraud is a felony.

After a period, a couple often divorces if the marriage is no longer useful.