Me and my friend had a similar issue - that she was round mine for a couple days and we wanted to play at the same time. Both of us have PS3 & PS4 versions, so while I'm now using my PS4 version she was going to use my PS3 version (which proved not so easy as we thought it would be due to my Square Enix account being automatically signed in)

We finally managed to sort it out by creating her an account on my PS3 and logging in on it with her PSN account (just using my User account on the PS3 and then signing in with her PSN account apparently didn't work). I think the game is linked to your specific PSN account, so if your mate played on your PSN account then his Square-Enix account will be linked to it. If there's a way to unlink them, I wouldn't mind knowing out of curiosity, but I couldn't figure it out if there is ...