Praise be to Allah.
If a wife with whom the marriage has been consummated becomes Muslim, and her husband remains a disbeliever, she becomes unlawful for him, and it is not permissible for her to allow him to be intimate with her. But separation and divorce should wait until the end of the ‘iddah, counting from the time she became Muslim. If he becomes Muslim before the end of the ‘iddah, then the marriage remains in effect. If he does not become Muslim before the end of her ‘iddah, then she is in charge of her own affairs and it is permissible for her to marry someone else.
Ibn Qudaamah (may Allah have mercy on him) said in al-Mughni (7/117): If one of them becomes Muslim after consummation of the marriage, then there are two reports narrated from Ahmad regarding such cases, one of which says that they should wait until the ‘iddah ends; if the other spouse becomes Muslim before it ends, then the marriage remains in effect, but if the other spouse does not become Muslim before the ‘iddah ends, then they are separated (and divorced) and the separation is regarded as having begun when one of them changed his or her religion, so there is no need to start counting the ‘iddah again. This is the view of az-Zuhri, al-Layth, al-Hasan ibn Saalih, al-Awzaa‘i, ash-Shaafa‘i, and Ishaaq. Something similar was narrated from Mujaahid, ‘Abdullah ibn ‘Umar, and Muhammad ibn al-Hasan. End quote.
The scholars of the Standing Committee for Issuing Fatwas were asked: What is the ruling on a Christian woman who becomes Muslim, and is married to a Christian man, and after declaring her Islam she wants to marry a Muslim man? What is the Islamic ruling on this case?
if a woman who is married to a disbelieving man becomes Muslim, then she becomes unlawful for him and their marriage ends. However, she should observe ‘iddah. If her ‘iddah ends without him becoming Muslim, then she is divorced from him, but it is a revocable divorce [and she could go back to him if he becomes Muslim after the ‘iddah is over], because Allah, may He be exalted, says (interpretation of the meaning):
“And if you know them to be believers, then do not return them to the disbelievers; they are not lawful [wives] for them, nor are they lawful [husbands] for them”
If he becomes Muslim before her ‘iddah ends, then she may go back to him as his wife, because the Prophet (blessings and peace of Allah be upon him) allowed the Muhaajir women to go back to their husbands when they became Muslim before the ‘iddah ended. End quote.
Shaykh ‘Abd al-‘Azeez ibn ‘Abdillah ibn Baaz, Shaykh ‘Abd al-‘Azeez ibn ‘Abdillah Aal ash-Shaykh, Shaykh Saalih ibn Fawzaan al-Fawzaan, Shaykh Bakr ibn ‘Abdillah Abu Zayd
Fataawa al-Lajnah ad-Daa’imah, 19/20
Thus you will know that it is permissible for this woman to get married after her ‘iddah ends, and there is no need for a divorce from her non-Muslim husband. But because her marriage is officially documented, and she is in a non-Muslim country, there may be a need for proof that she is separated from her former husband, so as to avoid any negative consequences that may result from her getting married without this proof. In that case, the non-Muslim husband should be persuaded to provide some proof that they are indeed separated and divorced, or she should obtain documentation of the separation by whatever possible means, even if that is by paying money to the husband.
There is no need for ‘iddah after obtaining this documentation, because she became irrevocably separated from him once her ‘iddah ended, which was counted from when she became Muslim.
And Allah knows best.