Should a Muslim woman who has recently converted to Islam be informed that her husband must either convert or separate from her, and what is the best way to convey the Sharia ruling to her in this situation?

First: Islam does not permit a Muslim woman to remain married to a non-Muslim under any circumstances, based on the verse: (Then do not return them to the disbelievers; they are not lawful [as wives] for them, nor are they lawful [as husbands] for them). This prohibition may be a reason for the husband's conversion to Islam, as happened with Zaynab, the daughter of the Prophet (peace be upon him), and Umm Sulaym. Whoever chooses Islam must submit entirely to its rulings.

Second: As soon as the wife embraces Islam, her non-Muslim husband becomes unlawful to her; this is by scholarly consensus. If the non-Muslim husband embraces Islam while the wife is still in her waiting period (iddah (definition)), they remain married. If her waiting period ends and he has not embraced Islam, she is free to marry someone else, or she may wait for him, hoping that he might convert.