What is the ruling on a woman who betrays her husband via chat and wishes to return to him after he has divorced her twice?

A woman's speech in chat and elsewhere, if it contains anything unlawful, is forbidden. If she falls into adultery or its preliminaries, it is even more forbidden, and the sin is magnified if she is married. Mere regret is not enough for repentance; rather, it must be accompanied by abandonment [of the sin] and a resolution not to return to it. A wife must protect her husband in his absence, as Allah Almighty said: "So righteous women are devoutly obedient, guarding in [the husband's] absence what Allah would have them guard."

If the woman has been divorced twice, do not hasten her return until you are certain of her repentance, sincerity, and rectitude. If she becomes righteous, then keep her, treat her kindly, and be a good example for her. But if she persists in her deviation, then it is better to divorce her.