Most Helpful Girl
I wouldn't buy it. She probably cheated and tried to cover it up by saying it was her friend's. Well, if it was her friend, then he/she would probably have logged out after being on her pc for a while, since most people log out. But it's all just weird. Facebook is also on phones so why would the friend use her computer?
Most Helpful Guy
The trust is broken. You won't believe her unless she tells you what you suspect. Here is all that is left to say:
"I know you are lying. If you can't come clean about it, that's your choice but my choice then will be to end things. I can't be with someone who will not be honest with me. But, if you come clean, we can talk about what I need from you moving forward and what the boundaries will be in this relationship until I can trust you again. So let me know how you want to handle this."
Obviously, at this point she has the choice to walk away or deal with the consequences of broken trust in the relationship. But standing your ground with her is important. You don't have to stay in this relationship or accept a lie, but you don't get to stay and not deal with it and make it awful for the both of you either.