Generally speaking,, a $10 letter will get you the following,, according to the info you provide & the serial number; (Type of gun and caliber.)
(1) The correct model nomenclature. (Example; BKH-44)
(2) The manufacture date. (month & year.)
(3) The shipping date. (month & year.)
(4) The place the gun was shipped to originally.
Sometimes,, if there is something special, AND it doesn't violate privacy etc,, you may get additional info. But what I listed above,, is pretty much normal.