Hi Greg. Welcome to the forum.

Yes, all original 620A trench guns should have matching numbers on the receiver, stock and barrel. A few other parts also have the entire or a partial serial number.

The stock is numbered on the end that attaches to the receiver. You might have a tough time getting the seller to agree to remove the stock, especially if the gun is original and in excellent condition.

The barrel serial number is on the barrel head in the action bar slot.

All 620 trench guns have a matte blue finish, plum colored bayo adaptor, and ploished blue heat shield.

Guns with serial numbers from about 26,500 and higher should have an "S" marked bayo adaptor.

Do you know the serial number of the gun?