I would rather know. A million times over. Dp's cousin tried it on with my mate, who said "er is your gf not due to have your baby in the next week? And currently at home minding your kids?". He's an utter slime ball. It's killing me not being able to warn the gf, who thinks he's changed his ways, they're all loved up on fb, yet he was trying to put his hand down my mates top a few weeks ago 
If my mate decided to tell her, and his gf asked me outright, I wouldn't lie.
I think it has to come from the ow herself. And you have proof. I would send a cropped bit of one of the screenshots and tell her you have more, if she wants to see, so she knows you're not lying.
A few years ago, I caught dp having an emotional affair building to more, lots of flirty messages, running me down etc, and he denied everything. But I'm not daft. The woman didn't admit anything (to a mutual friend) until after we'd broken up. If she'd told me at the time when she started to feel guilty/ realise it was getting inappropriate, it would have given me so much validation. At one point I was so confused, accused of being paranoid etc. Her admission came too late, I'd already sussed what was going on, we'd broken up and I was trying to move on. We talked about it when we got back together, and he knows it was wrong, mostly the lies and denying. If I got a message like this I would bin him straight away. Worst thing to me would be to find out in 5 years, he'd had a string of women, and everyone knew but me.