Most Helpful Guy
They can do that, but realize that it's a huge invasion of privacy and trust. Is this girl he used to "hook up" with someone he was in a relationship with or someone he just had casual sex with? If he was just in a relationship with the girl before and still talks to her you really shouldn't do this, plenty of people stay in contact with their past lovers and it doesn't mean anything is going on. Of course if he was having casual sex with her that's a larger red flag and I would try talking to him about and see what he says, if he's the type of guy that cheats/lies/hooks up with random girls then you're probably justified doing it.
Remember that you're in a relationship, you need to give your partner the benefit of the doubt in most cases. Going through their texts is pretty much akin to say "I don't trust you at all", of course if the person isn't trustworthy and hasn't earned your trust then it's probably acceptable1