Is it permissible to marry a foreign woman who has embraced Islam and does not live with her non-Muslim husband, with whom she has children, while concealing the legal aspect of the marriage due to her circumstances?

If a wife converts to Islam while her husband remains a disbeliever, she becomes unlawful for him. Her 'iddah (waiting period) ends with childbirth if she is pregnant, or with three menstrual cycles if she is not pregnant. She is permitted to marry a Muslim man after the 'iddah expires, and there is no requirement to wait for an official divorce, though it is advisable to wait for the civil contract to conclude to avoid legal issues. It is not permissible for her to marry without a guardian (wali). If there is no Muslim wali, a Muslim judge (qadi) or his representative shall act as her guardian. If the marriage is conducted with the guardian's permission and in the presence of witnesses, it is valid. Announcing the marriage is recommended.