He wants to marry a non-Muslim woman who became Muslim, but her husband has not divorced her

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?

They replied:

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”

[al-Mumtahanah 60:10].

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.