Most Helpful Girl
Well, now that you mention the element of the fact that he doesn't have a Facebook, it does seem a little strange, almost like she wanted to send a message and hopes it gets to him, but I don't think it's strange that she'd want to.
Just because a relationship doesn't make it doesn't mean all the love and emotions associated goes as well. There may be some residual desire there which isn't entirely suspect. Has she given you other reasons to feel insecure about this? If it's an isolated issue or situation, I say worry no more.