It’s probably a genuine Gibson, even with the possibly-suspect inked-on serial number. The problem is: You can’t really put a Floyd on a Les Paul without first reducing the angle of the neck joint to make it work properly. A Les Paul cap and neck angle are not designed to accept an aftermarket through-body vibrato system. That’s why Gibson created the Axcess model to overcome that problem. Not surprisingly, they include no photos of the back to show you what kind of a hack job was done to get the Floyd and springs in there. My guess is it plays like crap. I wouldn’t be mounting a lock nut anywhere on that delicate headstock behind the factory nut either. The factory nut should’ve been replaced with a Floyd nut. Don’t bother with it unless you want to un-do that whole mess and restore it back to factory spec.
Real. Look at the headstock construction - the wings are there which I have never seen any fakes have. You can remove all doubt if you see what's in the truss rod cavity. Better have a 5/16" nut... The inked SN isn't something to run from. Imported fakes generally etch the SNs from what I've seen. Either way, I would be inclined to believe it has been modified.