DH started a new job about 9 months ago, as a very senior manager. The person in the role before him was incredibly damaging, so all the staff have taken to DH like he is the 'wonder kid' (he is very friendly, approachable, and as he wants to be liked by everyone he can sometimes do too much for them).
Now, DH has a particular manager under him who I now callhis "granny stalker". She is about mid 50's, is married, and has kids and grand-kids (hence the granny reference). I have met her once - she seems nice enough, but is not the most attractive lady. DH is 43 and exceptionally fit and quite attractive. I'm 38, 36 weeks pregnant - and currently resembling a human grapefruit

So, this manager was initially relying on DH to sort out some major staff dramas she has been having. He did a great job, and she now idolises him. Since then she would text and email him daily about completely random stuff (I have seen some texts and emails, as DH and I are very open with our phones, email etc, know each others passwords, will answer each others calls and texts if they are not work related etc). DH would contact her back, nicely, but in my opinion he "fed" her a little bit by responding to every message she sent him, even if a response was not (IMO) needed. We are talking
up to 5 emails and 2-3 texts a day, at this point.
In the last 2 weeks, she has been getting more...intimate? DH went to a staff function at her place, on a Sunday, and took DD (2) with him. I was at home, too tired to do the 3 hour round trip. After he got home she was sending him multiple texts about how beautiful DD is, "just like her daddy", as well as photos of the dessert he missed in leaving early, how she wished he could have stayed etc. These texts went well on into the night, even though she was still hosting the party. After this, I called her the "stalker granny" and he started to as well.
After this work function, the texts and emails seem to have become even more prolific (now up to 10 per day). They often (but don't always) contain references to how fantastic DH is, how attractive, but are still 'borderline' in terms of being inappropriate. There is a lot of good natured teasing as well, which he joins in on, but is never inappropriate himself (that I have seen - I have not actually checked every text or email, but know about the ones he has shown me or I have picked up when his phone beeped).
Last night was my "straw meet camel" moment. He got a text at 9:00 pm, and when I asked who it was he said "Guess". It was her - she is away for work, and was (apparently, I didn't actually read the text) contacting him to say she had just gotten some really nice lollies.
Umm...HUH??? Is it just me, or is this starting to sound a little...off? Maybe it's my hormones talking. But then again, I think if she was younger and more attractive, I'd be much more suspicious (and worried). And then my experience with EB tells me that men will behave inappropriately with women who are older/less attractive than their current partners, and to think "Well, nothing would happen as she is a grandmother and less attractive than me" is idiotic.
For the record, I 99% trust DH. Not 100%, because I have been hurt by people lots in my life. But I don't know that I'd trust
her in this situation. I really don't know what she is playing at - is it harmless flirtation, or something less harmless? I have told DH I'm concerned, and that he shouldn't "feed" the relationship more than his working partnership requires, but I said it rather casually, and am starting to think I need to say something more firmly. I guess I'm worried it will get more intense (although I'm not sure exactly what I mean by that), and then - who knows? At the very least, I can see it potentially damaging his working relationship.
So, what do you think? What would you do?