my comments...
1) ex-colleague joining bf's company. So? Why cannot tell bf? I don't see the need to hide anything. I don't think its his gf that thinks he is stupid. If he is upset with that, the natural analysis and conclusion is that he is indeed stupid.
2) So, this ex-colleague likes his gf and doesn't backs off. BUT, does this has anything to do with employment? The answer is no. So, what's the problem? He should be more concerned if this ex-colleague hasn't quit and is facing his gf everyday. But not when he is becoming his colleague instead.
3) what should he do?
Nothing. Be completely professional. Nevermind their personal differences. Just continue working and treat him just as another colleague in office. It doesn't matter if personally, he finds this colleague morals sucks. This has NOTHING to do with his job and career.
4) Lastly, Ta Ren, what does it gotta do with you? The story isn't complicated but the one telling it is making it complicated. Is actually a very simple thing. gf telling bf this new colleague of his was her ex colleague that has shown interest in her. That's not stupid. That's being pretty transparent about information. That's good. Avoid the need to guess and finding out by himself investigating and probing.
And its the guy's issue if he cannot even deal with his insecurity despite his gf coming clean and volunteering information. To me, that's a real loser.