This dude already is bullshitting his wife about the cheating, and doing it badly. He doesn't care enough to hide his infidelity, and he clearly doesn't think much of his wife's brains.

If she starts checking his phone he's going to spin this to everybody - their family, their friends, his girlfriends, and yes, her - as "she's controlling, she's paranoid, she's jealous" and people will fall all over themselves to reassure him that he doesn't deserve to be treated this way.

I'd recommend couples therapy, but I don't think that's going to do much good either. He's practically rubbing her nose in the affairs as it is. If he cared about her feelings even a little, he'd put the bare minimum effort into hiding them, but he doesn't.

She should leave him, period.