nice find - one of my favorite grouse guns is a 16ga 1904 VH
what is the frame size (marked on a barrel lug) and the barrel length?
if you give the serial number we may be able to confirm the original configuration. a visit to the Parker Collector Board will tell you if any factory records exist.
how are the barrels? any pitting? is the gun on face?
check the chambers, they may not be 2 3/4
if any thing rates as a common problem - the head of the stock sometimes splits on a Parker (but a small percentage)- I suspect, but cannot prove, a combination of heavy loads and oil damage, this can be neatly repaired leaving little evidence, although the normal approach is simply a bolt through the head.