Is there a plugin or anything that makes it possible?.
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I have seen others use the tutorial on PHP + leaderboards and integrate it with facebook to show the users profile picks next to their high scores. If you look at Tappy Shark on facebook you will see what I am talking about. That game was made in C2 and uses php + facebook integration to do it.
What about cocoonjs compiled apks?. Can it work on android devices.
Not sure, I haven't seen anyone try that yet. There may be a thread in the forums on it though, just search for CocoonJS + Facebook