How would this make you feel?

I absolutely wouldn’t like and it would be a big quarrel in our house. I would want husband to txt her not to message him and block her for a start. Not sure about going to HR depends on situation at work.
Call me possessive, controlling or whatever but it’s what I would do. Mind you I would do the same if a male colleague was txting me and I wouldn’t need my husband asking me to do this.
However if your DH is very non confrontational type may be that’s why he hasn’t done it yet.

What did you say to her to address it? What was her response? It's completely disrespectful of her to be messaging your husband. I wouldn't tolerate it either OP, completely agree with you.

I don't think it's that unusual to message daft things when you're drunk, she probably messages lots of people.

MAYBE she is attracted to DP BUT the fact that he doesn't reply, he hasn't hidden it, you know her also and the messages don't seem to be sexual/innuendo I don't think he's done anything wrong.

To me it seems like she is attention seeking but it doesn't appear that DH is playing along, he just doesn't want to make a big deal. I'd probably ignore the messages too and leave it at that.

This sums it up perfectly.

Try not to worry and escalate this into something especially as you all work at the same company and he is her manager.

I’m with you OP, I wouldn’t like it. I specifically wouldn’t like it more from her part. He’s done the right thing, ignored her and been transparent with you about it. I understand it’s a bit awkward for him to outright tell her not to.

This sounds really bitchy but I would make a joke in front of her about it to embarrass her, “you going to talk to yourself in my husbands inbox after you’ve had a drink again haha”. It keeps it lighthearted but also makes her feel a bit silly for doing it, especially when she’s not even getting a response. I wouldn’t like to directly say “you need to stop” as it feels a bit heavy and I’d hate to come across as insecure about it.

Just my view but I agree it would piss me off that she’s doing that

Well she does get it. Doesn't she.

I agree that it doesn't seem like your DH is playing along with this. I suspect the reason he hasn't addressed it is simply that it's very awkward when someone you manage is also a friend. He probably doesn't want to get into a painfully strained conversation in a meeting at work where he has to address inappropriate behaviour with a female colleague who is/was a friend. So he's been ignoring it.

I personally think that messaging random shit like that when drunk to someone you work with is, as you said, embarrassing. It's immature, attention-seeking behaviour. The message that said 'Boring' when he'd left a work event early seems totally fine and normal to me, but the stuff about her pillow and stuff is just cringe. But he doesn't seem to be engaging with it so I don't think he's done anything wrong.

She seems immature.

I think I'd be ok with occasional daft drunken messages that he wasn't responding to TBH.

'My pillow is cold' when they are presumably staying in a hotel together is a come-on, surely? I'd suggest to DH that he asks her to stop messaging him outside working hours because he's her line manager and is therefore inappropriate. The main thing is that he doesn't seem interested in this woman but she's out of order doing this.