Should the female friend reset the password for her ex-fiancé's Facebook account, knowing that he might resume his forbidden conversations, and would she bear sin for that if she reset it?

Acquaintance and a love relationship between a man and a woman who are not mahram is not sanctioned by Islamic law, and it is a door to temptation and corruption. Whoever is in such a relationship must repent and sever it. If he is a suitor but has not yet contracted marriage with her, he is still a stranger to her. Do not restore the password to him as long as he uses the account for forbidden relationships. As for your problem, send it to the website for a private answer.