How can a fiancé be convinced to adhere to the hijab and modest Islamic dress in a Western country, and to conduct himself in accordance with Islamic Sharia?

The way to convince him is to inform the suitor that the hijab (definition) is an obligatory duty upon the Muslim woman, and that it is not permissible for her to display her adornment in front of non-mahram (definition) men. Her displaying adornment in front of non-mahram men is a major sin that incurs Allah's wrath upon both the husband and the wife. As for listening to unlawful songs, it is a great sin and a grave transgression. If the suitor insists on her removing the hijab, then the engagement must be annulled without hesitation, for such a person is not suitable to be a husband.