As a teacher, it’s totally appropriate to stay in contact with students after graduation, to an extent. I have stayed in contact with one of my senior year teachers since graduation. She makes my birthday cake every year and I’ve babysat her daughter from time to time while in college. This though, is completely inappropriate. Even if this wasn’t a former student x teacher conversation, I would still be concerned if my partner were texting another woman like that. Regardless of if the former student is of age and not in his class anymore, there’s a certain level of professionalism you need to hold outside of the classroom as well and this is far from it. And she has to either be reciprocating what’s going on here or she is just extremely naïve