I don't really see a problem. If the police did nothing and he actually sent it, then people would throw a bitch fit. Especially, if the girlfriend got hurt by him. So, we can't blame the police.
The girl had no way of knowing whether he sent it or not, so can't blame her.
Guy is a scumbag, otherwise he wouldn't have the restraining order against him. But the charge against him will be dropped. He could also have a suit against google+ to recoup that $500.
It will work itself out.