ANSWER:

If a man divorces his wife in a sharia court, they are divorced.

He can marry a Christian or a Jew only. She can’t marry a non Muslim as this is blasphemous and invalid if she believes it to be permissible.

If a couple get a fake divorce letter from shariah court to prove to an international govt that they are not married then go ahead and marry different spouses to gain benefit of residency using that fake divorce letter. What is the status of their real marriage. The fake spouses are both non Muslims but the couple in question are Muslims.