What is the ruling of Islam concerning the marriage of a Muslim woman to a polytheist man after his conversion to Islam? Is it permissible for her to marry him if he embraces Islam? And how can she verify the sincerity of his conversion?

It is not permissible for a Muslim woman to establish a relationship with a non-Muslim man if this relationship leads to khalwa (private seclusion), touching him, or looking at his 'awra (private parts). The intention of marriage does not make this permissible for them, and she must immediately cut off the relationship with him. If he embraces Islam genuinely, then there is no harm in her marrying him. However, it is advisable to exercise caution and ensure the sincerity of his conversion to Islam and his good conduct.