I dont do the friendship with exes thing and I dont get with people who do. I feel like if you are romantically involved with someone, most of the time, you cant be real friends after. And why would I want to be friends after? I have real friends. I understand that is not true in every instance. But to each his own in that department. You just have to know what you are willing to accept.
It seems that you cant accept it. It seems like he knows this but he has text her anyway. To me that says a lot about how much he values the relationship if he would risk your relationship for a birthday text. People may think that is bogus to get upset about but when there is no reason to keep a door open but someone insists on keeping it open despite their partner’s discomfort, it speaks volumes. Also, he lied by omission and is hid something. You shouldnt have snooped either. But that just says you dont trust him.
So he lies and hides things from you knowing they are things that could hurt the relationship. You dont trust him. Move on, honey. Good luck!
You don’t trust him so you snoop through his phone. He doesn’t trust you so he deletes texts. Without trust this is already a failed relationship. It won’t get any better. You may as well breakup instead of dragging this out longer and have both of you getting more and more unhappy.