Are you sure the guy she met is a boyfriend or is he just a friend?

If he is a boyfriend, then don’t write the letter. Actions speak louder than words ~ there’s no point. Maybe she wanted to contact you to tell you she met someone. Don’t even give her the satisfaction. Move on.

If he is just a friend or an ego boost, and you don’t want to deal with her anymore, write the letter.

If you do want a relationship with her, or just want to figure out what’s going on, forget the letter. FB her, call her on the phone, see her. There might be more than meets the eye.