The OP does have a point. If, and it's a big if.
The letter is portrayed as a " letter of authenticity ".
I have read that already, so it's possible to happen.
Given the OP description and what others have posted about the criteria required to authenticate a particular item.
I would prefer and consider a historical letter from Mr. Jinks as a letter of origin.
It's how it started its existence, nothing more, nothing less.
Does it match that original description, that's up to whoever's looking at the gun.
Just a simpletons .02.
Have a great day.