Is an 'urfi marriage to a Christian man who verbally declared his conversion to Islam, without official proof, Islamically valid, or must they be separated?

The marriage contract is valid if the man's Islam is established before the marriage by the testimony of two just witnesses, and he is obligated to perform the religious duties, the most important of which is prayer. However, if his Islam is not established, the contract is void, based on the Almighty's saying: (And do not marry [your women] to idolaters until they believe). For the validity of the marriage, it is stipulated that the woman's guardian performs the contract, as the Prophet (peace be upon him) said: "There is no marriage except with a guardian." If the marriage is without her guardian's permission, it is void. The guardian is: her father, then his father, then her son, then his son, then her full brother (from both parents), then her paternal brother (from the father only), then their sons, then the paternal uncles, then their sons, then the father's paternal uncles, then the ruler.

If the marriage is legally valid and was performed by her legal guardian in the presence of witnesses but was not documented, it must be documented to guarantee legal rights and the lineage of children. His religion must also be changed in official documents.