Lisa, sorry to hear that. Your great grandfather's would be from 1889 and the F means it was an F Grade, which was the lowest priced hammer gun made. Cost then was $55.00 which was a great deal of money back then.
This would be a very early Fulton gun or what is called a Transition gun. This means that when L.C. Smith sold the guns works to John Hunter in 1889 along with all the unfinished guns and machinery, the guns were finished but there was no makers name on the top of the barrels. The Syracuse guns had L.C. Smith Syracuse, N.Y. on the top of the barrels. I don't believe yours has any name on it. The description would be; 5 pin 2 screw bar action lock, meaning the mainspring is before the tumbler or action, the for-end grip would have a vase or bell shaped ebony tip. The original butt plate would have a setter on point with it's right foot on a rock. The wood for both the stock and for-end would be decent walnut with fine checkering. The barrels would be Good Damascus.
I hope this helps and any other questions you could ask here or email me through the envelope after my name.