Yes, Stencyl's behavior create the screenshot and make an actor ( the empty ractangle for example) as screenshot graphic. It's very flexible because You can then scale this actor etc.
So, maybe there is some way to connect this actor with Your extension and after facebook login, wil be possible to create facebook post with such screenshot actor bitmap. It could be very good promotion for our games, specially that it is possible to make an screenshot of some funny moments in our games ( just adding small photo camera button, You can create some pictures and then after You login to facebook, You can choose which screenshot You would like to add)