Iphone apps for to save text messages?

OK so i feel my girlfriend is sending messages to a guy and deleting them after and so on…

is there a app i can install on her iphone to save all text messages in a file so even if they get deleted i can open the app and still see what's going on?

No, there's not. Has she started hiding her phone from you, taking it everywhere with her, or all of a sudden create a pin to lock the phone? If she is displaying different phone behavior, then the best thing you can do is communicate. Otherwise, leave her if you can't trust her. It's not worth the headache, trust me… Been there, done that.