Seriously, this is a major red flag. You aren't entitled to breach your lovers privacy.
That said I haven't read the article so maybe he's a serial killer or some shit. (I've never even heard of the website in the screenshot.) Either way, don't do that.
It's just the typical "I found a person I knew from a long time ago and we got together. Everything was good until we started to not get along as well, and I found out he's talking to his ex"
But the somewhat good news is that the boyfriend gave her the phone to look at facebook or smth, but the bad thing is she immediately went to messages instead.