Looking for information on Great Grandfather's Shotgun

[mmpalbq]

Would like to find out more about this shotgun.
overall length is 54 1/2 inches
Barrel length is 37 inches
Single Action shot gun
Lever action
This is the information on the stock right behind the hammer
Remington Il (something) U.S.A.
May 32 Nov 16 ----64A----1866
(other numbers or letters can't make out).

Thanks for any help.

[oneshot onekill]

Sounds like a Model 1893 or a Model #9. The marks should Be :
Remington Ilion NY. U.S.A. and the numbers are most likely Patent dates. FWIW