Is emigrating to a country where a non-Muslim woman lives, with the intention of introducing her to Islam and marrying her, while fearing the severing of ties with family and kin, contrary to Islamic Sharia, and what is the ruling on that?

A man's call to a woman to the truth is permissible, but it is better for a man to invite men and a woman to invite women, in order to avoid temptation. What was mentioned about the exchange of love between you is an unfavorable indicator, and it must be avoided, while it is possible to guide her to reliable da'wah websites. As for migrating to infidel countries, it is fraught with dangers, and scholars warn against it unless there is a necessity. Traveling specifically to invite this woman is not a necessity, as alternatives exist, and Satan may lead the caller into temptation.