Why not just sign the content with a digital signature?
Except it wouldn't change anything. Facebook doesn't care about fakes and people wouldn't care whether the picture someone shared hasn't been tampered. Also whoever manipulated the picture could just sign it again probably.
The challenge is establishing an author's credibility in the first place. If I trace a cert back to joe schmo off the street or some empty front business, then I'd probably not trust the content.