I feel very strongly that it would behoove you to have him read this thread and see some "experienced" folks' responses to what you've written....
After knowing this latest bit, that the woman has a HISTORY of lying, cheating, and deception, I personally would want zero involvement with her. I wouldn't forbid my boyfriend from dating her (I don't think a person can "control" a significant other), but I would, as you've done, tell him that I would no longer be involved with him if he chose to date her. We can only control our own involvements, and I, personally, would not date someone who thinks it's okay to date a deceptive cheating liar.
Make sure he knows he can do better than this woman. And make sure he knows that someone with a history of horrible relationship decisions (cheating, lying) might well continue the same. If she could cheat with her best friend's husband, what else could she be capable of? Could she lie about her STD status? Could she have intentions to cheat with him against you?
Why don't you suggest to your boyfriend that it might be fun and worthwhile to seek out more polyamorous folks for friendship, and start trying to get to know people with greater integrity than this (scary) couple? It might just be that he thinks that polyamorous folks are rare, and this is his "only chance". But really, he can do better than settling for these low-lifes.