Hey! This is kind of an old question, but I thought I'd share my solution anyway.
I couldn't get an official FB api to work, but through this tutorial: http://www.exploreroute.com/simplest-way-to-share-score-on-facebook-with-unity/ I managed to use FB url redirection on Godot too. I have this function on Global:
func share_on_fb(app_id, link, quote, picture, name, caption, description):
quote = quote.replace(" ", "%20")
name = name.replace(" ", "%20")
caption = caption.replace(" ", "%20")
description = description.replace(" ", "%20")
OS.shell_open(share_dict["http"] + "app_id=" + app_id + "&link=" + link + ""e=" + quote + "&picture=" + picture + "&name=" + name + "&caption=" + caption + "&description=" + description + "&redirect_uri=" + share_dict["redirect_uri"])
And then I use it on the "Share" button. You have to get a FB Developer app working, though - it's nothing complicated, but you need the App ID.