Is a marriage contracted between a man and a woman, neither of whom prays, legally permissible, and is it permissible for the man to reconcile with his divorced wife after his repentance, and what is the ruling on a reconciliation that took place without adhering to what is required by Islamic law?

Abandoning prayer is one of the gravest sins. However, the majority of scholars hold that one who abandons prayer, without denying its obligation, does not commit apostasy that expels them from the faith. If the abandonment of prayer was due to laziness and not denial, then the marriage is valid and the divorce is considered binding. The wife has become irrevocably divorced by the three pronouncements and is not lawful for him again until she marries another man, and then is divorced by him or he dies, and her 'iddah (waiting period) expires.

As for the questioner's belief that one who abandons prayer is considered an apostate, this needs clarification: Was this belief present at the time prayer was abandoned, or did it arise after repentance? Indeed, whoever undertakes an action believing it to be an act of apostasy has committed apostasy.

The questioner is advised to consult scholars directly or a Sharia court to clarify the matter. He should not base a ruling on the invalidity of the marriage that aligns with his desire after the divorce, as long as he believed in its validity before that.