So I can add people from Facebook via the Friend Finder in the client...?

But the Friend Finder in the client can't identify pre-existing friends' names that I have on Facebook and that have the Friend Finder enabled in their clients?

Might wanna look into that. Sometimes I'll come back on after a break from LoL to find an IRL friend who's changed their name and have to go through the awkward "who are you?" conversation because I don't recognize their Summoner Name anymore and people don't tend to keep their old Summoner Names as their statuses for much longer than a week or two.