I tried to find a simple shortcut to submit a post or save a post on Facebook. However, it seems Facebook is ultimately for mouse users.
What I found:
The only "workaround" I came up with: Hold Shift and hit Tab 3 times, then hit Enter.
But a shortcut like on the Stack Exchange sites, Ctrl + Enter would be a great time saver.
PS: One idea is to use a user script, e.g. https://greasyfork.org/en/scripts/2711-ffixer (it enables many shortcuts, still the post shortcut is missing).