What is the ruling on a wife seeking divorce from her imprisoned husband in order to marry another man who can help her raise her children, what is the ruling on this man, and is this considered incitement?

It is not permissible, شرعًا (religiously), for a Muslim man to propose marriage to a married woman, whether her husband is absent, imprisoned, or involved in a dispute. This is due to the severe warnings against instigating a wife against her husband (تخبيب المرأة على زوجها) and the prohibition against a woman seeking divorce from her husband without legitimate cause (بغير بأس). The فقهاء (jurists) have agreed on the prohibition of proposing to a married woman, whether explicitly or implicitly, to prevent evil and corruption.

The proper course of action would have been to let the wife decide to separate from her husband by requesting annulment (فسخ) or divorce (طلاق) from the شرعي (religious) judge. After her waiting period (عدة) concludes, there would be no harm in proposing to her. However, promising her marriage while she is still married to her husband is an aggression against sacred honors (الأعراض المحرمة) and a grave sin.

Whoever has committed this must repent and seek Allah's forgiveness, resolve not to repeat it, perform many good deeds, and show kindness to the imprisoned husband. If marriage takes place after her divorce and the expiration of her waiting period, then it is a valid marriage (نكاح صحيح).