Should I wish my ex gf a happy birthday?

My ex dumped me in May, I've been having a really hard time with the breakup. I was so obsessed with her even while we were dating she was exactly my type, but we only dated for a few months and I found out she was just using me as a rebound. She's reached out to me apologizing for everything and just checking in on me. I've missed her since she broke up with me. Her birthday is coming up in a few days and was thinking about texting her happy birthday, is this a bad idea?