In general, there are a number of issues in this type of situation. How long were they dating before the breakup,how acrimonious was the breakup, who initiated it? I would discuss these things with my friend and then tell her this particular shidduch was redt to you, and you would like to go out with him. How woudl she feel about it? It might not bother her, if he was not for her. My nephew married the girl his best friend dated. It was the BF who made the shidduch.
In this situation, the girl still has feelings for the boy and HE broke it off. If this would cause great agmas nefesh to the other girl, I would not go out with him, unless you don’t care about losing a good friend. Guys come and go, but good friends are 4emant to stay. It’s a judgment call.