Now, with facebook and social media, it's easy to catch up with old friends and flames. I would compare the email your DH received to a FB private message; my SO gets them and I get them as well. As long as he doesn't keep texting back not meets with old flames, I'm ok with an occasional text, as I believe FB and others made this kind of contact seem less inappropriate. Not saying I like it, when SO gets that kind of message, but I dont' lose sleep over it or feel threatened.

My dh had an ex try this a few times. I asked him for his phone and sent her a wicked evil text "just because you are lonely and unhappy with your husband, please don't try and make yourself feel better by trying to play nice with me. We aren't friends and we haven't been for a long time. Take your putty party elsewhere". O

I would probably say something to my DH if I were you. It's obvious that he is not interested in her as he showed you the email to begin with. Men are so naive, I would tell him you think she is fishing and if she emails again he needs to make sure he tells her he is happily married. He probably didn't even think about that was her intentions but like some of the other posters have said, I've fished and been fished. Women do that. My SD16 BM fished her high school sweetheart out if his 20 something year marriage and is married to him now. Your DH just needs to nip this in the bud.

I think of it as poaching, not fishing: That "poaching" is a sign of poor character and bad morals. Weak-minded people try to take what others have. Strong people pave their own way.

A very similar thing happened with me not too long ago. Without going into the whole scenario when I found out that a particular woman was messaging and calling ‘MY MAN’ I explained to SO that I wasn’t happy about it and that I would like it to stop as this woman isn’t a friend only an associate and she had just recently broken up with her better half and is pouring her heart out on a shoulder that I should be crying on not her. Anyhow after I damaged my vocal chords, SO called her and basically told her that this ‘friendship’ is affecting his relationship and his relationship with me is too important to jeopardise it over this ‘friendship’.
If you are not happy for your DH to have any association with her than he needs to make it clear to her otherwise she will keep emailing etc and if he is anything like my SO he won’t do or say anything to her until he sees you hurt and upset over it. He doesn’t have to be rude to her about it but he does need to be firm and he does need to put a stop to it.