I don't think the claim falls apart on inspection - the fake FBI suicide story was shared 2.5 times more on Facebook than the fake Atlanta shooting story. Do you have any examples of liberal fake news that were as popular as conservative fake news?

FBI suicide, 569k: https://graph.facebook.com/?id=http://denverguardian.com/201...

Atlanta shooting, 222k: https://graph.facebook.com/?id=http://baltimoregazette.com/a...