My fiance's ex keeps trying to contact him

I guess my overall question is what would you do? I'm 22 weeks pregnant so my emotions are running pretty high and I need level headed people to give me some advice lol My fiance's ex has apparently always kind of "checked up" on him and asks him how his life is going, updates him on hers, etc. And he replies, answers her questions, is in general friendly. However after we got engaged I noticed a slight change in her messages (we lay beside each other at night on our phones and never try to hide what we do or who we talk to) she started adding "I love you" to the end of hers. He never seemed to think it was weird because he never said anything about it to me and never stopped messaging back, and he told her he loved her too...then she messages him all about old memories of their relationship and how much she misses him, this is when I finally confront him about it and tell him I don't feel like her intentions are good or like she's just being friendly. Ar first he defended her and said they've always talked and been friends but after I told him he'd feel differently if it were me and my ex, he realized I was right and hasn't messaged her back since. But she still messages him about how much she misses and loves him and the messages have only gotten more inappropriate in my opinion. He's too nice to tell her to stop messaging him, I think he also doesn't want it to seem like I'm the reason he's telling her to stop. But I honestly don't care what she thinks of me and just want to tell her to f*** off or even go as far as threaten her well being lmao but he trusts me enough to not act crazy and that's why he's so open and honest with me to begin with. But every time I see she's sent something new it fuels the fire, what do I do?