repents to Allah Most High and returns to Islam, he must renew the marriage contract. The same applies if it is the woman who does not pray.
This, however, is different from marriages concluded between non-Muslims while they are still in a state of unbelief. Suppose an unbelieving man marries an unbelieving woman and the wife later embraces Islam: if her conversion occurs before consummation, the marriage is automatically dissolved; if she converts after consummation, the marriage is not dissolved immediately. Rather, the matter is suspended: should the husband embrace Islam before her waiting-period expires, she remains his wife. If the waiting-period ends before he becomes Muslim, he forfeits all claim to her, because the marriage is deemed to have ended the moment she accepted Islam.
During the Prophet’s lifetime—may Allah bless him and grant him peace—many unbelievers embraced Islam together with their wives, and the Prophet approved their existing marriages, unless a prohibiting factor was present. For example, if both spouses were Zoroastrians who were related to each other in a degree of kinship that Islam forbids, they would be separated upon accepting Islam because the cause of prohibition remained.
This question is therefore not comparable to the case of a Muslim who apostatizes by abandoning the prayer and then marries a Muslim woman. A Muslim woman is never lawful for a disbeliever, by explicit textual evidence and by consensus, even if the disbeliever is originally non-Muslim rather than an apostate. Consequently, if a non-Muslim man marries a Muslim woman, the marriage is void and they must be separated; and if he later embraces Islam and wishes to return to her, he may do so only by contracting a new marriage.