well, this story seems somewhat fishy

why did the girl gave the password if she has such emails and conversations? is she trying to get rid of the guy ( showing her secrets because boys trust level is very thin)? 

And how stupid is that boy who is judging her with those emails and convesation without talking to her? 

Oh yes, he is sharing wiith his friends and his friend is making it public; very nice

C'mon, the main thing is "is she faithful or not?" and your friend can have a good conversation with her, ask her about emails and truth will be there on the spot

Like this, you will know what is girl trying to do and boy can decide easily