I had the same problem a while ago. Girl spent alot of time with a couple dudes and one in particular. I asked her about it she denied anything could/would ever happen. I took the attitude that there was nothing I could do and being jealous was conterproductive so I ignored it. Then I gradually found out more and more stuff between then that was arguably crossing the line if you know what I mean. She would talk to him about stuff she wasn't telling me. I knew he liked her and she denied it till he made moves while I was away. Surprise
She saw much less of him after that and finally believed me
We broke up a while later because of a bunch of reasons and that was actually pretty low on the list. To be honest though if your girl is not seeing what is obvious to you and perhaps to others then she needs to be educated or it will end in a mess. Having said that if she is already going to move in with him it will work itself out pretty quick for better or worse but always better in the long run.