The markings were used betw 1875 and 1887. So that dates the shotgun somewhat. The 'Not for Ball' marking started use in 1875.
'N' could be a bbl fitter, a filer or polisher. Could be a bbl grade marking. Not really sure.
The Elephant figure is a Greener trademark.
To the right of that is a Crown/BP,,,Birmingham Proof (Black powder)
The deep dot next up and to the right,, I don't know..
The 13B 14M stamping was a system used at the time of marking the bore dia.
It was was the measurement of the bore dia at a specific distance (10"?) from the breech end of the bbl.
The measurements were done with plug gauges. In this gun the bore would accept a 13ga plug,,but not a 14ga plug.
It means the bore dia at that point is somewhere between the dimension of 13ga and just under 14ga.
It's not at all uncommon for 12ga guns from that era to be marked 13 (tight bore),,or even 11 (oversize bore).
What did matter is that the size of the bore AT the Time of Proof was noted on the gun.
If the gun was later altered by honing out the bore, the alteration could be found by measuring the bore dia.
Alteration beyond a certain number of .000 put's the gun 'out of proof' under Brit Proof Law and the gun would be unlawful to be sold w/o first being reproofed.
Such a gun would have a second set of proof marks applied at the time of reproofing.
Even US buyers of British shotguns are real sticklers for their guns to be 'in proof'. While US made shotguns are honed and reamed out w/o a thought as there are no US proof laws.
To me, the same safety rules would seem to apply though .
WWG is back in the hands of a family member once again.
They do have the records of production and for a fee will provide info as best they can on any gun they have built going back to 1829.
Information
Nice shotgun and great see it still in your family.