Pre-1896 is the UK equivilent to our GCA 1968 pre 1898. I believe the reason the UK uses 1896 is that was the year Nitro-proof became optional. Lacking the words NitroProof indicate the gun is "most likely" pre-1896 and good enough for them. (UK folks can clarify)
Nigel Brown's Birmingham book has a paragraph on 1896 with markings.
I have brought back pre-1896 guns from the UK in my checked bags. The documentation that I provided customs, per gun, was:

1.) Bill of sale with gun description, SN and appx date of manufacture.

2.) A copy any pages from a published references supporting the claim of pre-1896.

The bill of sale is easy and make a copy for each gun.

Published references:
Either of Nigel Browns books or Boothroyds book are what I use.
You have several solid ways to ID the age of a British made gun:

1.) Date of manufacture list of serial numbers from an accepted reference book.

2.) Makers address from the rib. Since the makers moved around the address ties the gun to a certain date range.

3.) The Makers name. The name of some makers, say Joseph Lang, then Joseph Lang and Sons are specific to a date range.

4.) A last resort, look for patent numbers. British patents are protected for 14 years. You can look up the patent in Nigel's Birmingham book. If it was an 1874 patent and it is marked, then the gun wouldn't carry that mark after 1888. Copy the patent page.

I always put a copy of everything I could find with my paperwork. I put one copy in the gun case and kept one copy with me in my carry-on.

When arriving in the US, you have to declare the guns on your import statement. I always put x antique shotguns. Antiques are not taxed, so you should not pay any duty.

The worst you have to do is open your gun case and compare the supporting documentation with the actual guns.

If you need help ID-ing, post the makers exact name, address, SN, any patent numbers, and a photo or good description of the proof marks.

Sleeved guns often have their original proof marks still on the flats, so check for multiple proof marks to find the oldest.

Joe