OP very similar happened to my BF just when she was planning her wedding,the woman that contacted her wouldn't stop for months on end until I told my friend to threaten her with the Police,funnily enough she stopped straight away then.
She'd told my friend that she'd been having an affair with BF partner,all of the times and dates she'd given he was at work my BF pointed that out and the nasty bitch made out that she'd been meeting him at work in his lunch break but he worked with my BF and they always took they're lunch breaks together,she was obsessed she came out with all sorts of sick and twisted shit that she said she'd done with him/that he liked to do.
It went on for months and I did some snooping for my friend it turned out she was friends with his ex wife and had a thing for him,but the creepiest bit of all she'd never met him not even once she'd became friends with his ex wife a couple of years after they'd split up,all she knew about him was what his ex mentioned in passing and she didn't even know what he looked like till she looked for him on facebook and they lived hours away from one another so she hadn't even ever seen him in the person.
There was no other reason for it than she wasn't stable and not a very nice person to boot.
I've been on the receiving end of unwanted attention myself as well so it does happen.
I once kissed a guy on a night out(I was single)and that was that thought no more of it,untill a few weeks later when I go out again and find out from some members of his family that he's said were in a serious relationship,we are getting engaged,they were all so pleased to see me and I felt sick having to tell them the truth.
It took a few months for it all to come out but it turned out he'd been stalking me for months before I'd even noticed him around so the kiss was all it took for him to run of into some fantasy life and make up a false relationship with me,it got quite scary and it was only having friends that were in the club and pub buisness that kept me safe from him and warned him off.
It could be as simple as she's spoken to your DH online and he's been polite and nice and replied and she's gone of on a tangent of her own,for some people it can take next to nothing for them to convince themselves that they're in a relationship.
If it was me I think I'd play her at her own game and feed her some false set ups,things like "so he wasn't away with work on such and such date he was with you that night"?if she turns around and says yes then you know she's just a shit stirer.
If not that ask her for proof,she must have a text,email,message somewhere that she can show you and when she can't that same as above you'll know she's just a sad individual.
Either way whatever you chose to do I'd be making sure you both cut any contact with her and make sure you block her name so she can't find either of you on facebook as well.