Respectfully disagree back atcha. :) Sort of.
I do agree, someone should know that he's causing problems. If the guy works for the same company, or even a sister company, then it IS sexual harassment and your friend's supervisor should know. Who's to say he's not doing this to other women, maybe customers?
However, if the guy hasn't committed a crime, it's not right to report him just because he MIGHT. That way lies witch hunting and inquisition. Like, in that Tom Cruise movie (which I've never seen because I hate him, but you know) where people get arrested because the psychics say they'll commit a crime in the future.
Granted, if a person is exhibiting signs of imbalance, they should be watched. But from the very little I know about this situation, so far the guy has just overtexted and sent unwanted nudes. A lot of "normal" guys do that, it doesn't mean they'll soon stalk or rape or kill. Plunging someone into the penal system (something I HATE) before they break the law is not cool.
Your questions were "What should she do? Is his behavior sexual harassment? Should I stay out of it?"
She should tell her supervisor and bring work authority into it, If she chooses not to, though, that's her choice.
His behavior MAY or MAY NOT be sexual harassment.. it's sounds like it's on the line from what you say, but we of all people don't know the reality of what's going on. You may not either, to be honest. So, Questionland can't answer that.
Should you stay out of it? Still, unequivocally, yes. Your friend "insisted" that you not get involved, and I strongly believe you should respect that.
I know it's maddening, and we all want to protect our friends. You're a good person for caring and wanting to help. I just think that you sound a little overly worked up and need to let her handle this on her own. The guy hasn't presented more than a social problem to date.