How can a Muslim man who civilly married a Christian woman in the West have his marriage contract registered Islamically after they move to live in an Arab country?

A legitimate Islamic marriage (Nikah) has pillars: the presence of the woman's guardian (Wali), along with two just witnesses, and a formula indicating the contract. If the aforementioned civil marriage was concluded with these pillars fulfilled, then it is a valid contract, and its effects are binding. However, if it was conducted without the attestation of two just witnesses or without a sufficient formula, then it is void, and cohabitation thereafter is forbidden. Its registration alone is not enough; rather, the husband must immediately separate from the woman before performing a correct, legitimate Islamic marriage contract that fulfills its pillars. It is permissible for a Muslim man to marry a chaste woman from the People of the Book if the pillars of the contract are fulfilled, with the caveat that documentation of the contract is not a condition for its validity, but rather for preserving rights.