Here is an interesting Brotherhood of Locomotive Engineers 40 year membership badge in silverplate awarded in 1911, most examples of these badges were gilt, and they started presenting them in 1903, the 40th anniversary of the organization.

It is inscribed on the back:

Born Aug. 22nd 1838, Little Falls, NY
G.A. Moore
1864-1911
Division No. 14
Ball & Co.

My Brotherhood of Locomotive Engineers Directory indicates that Division 14 was located in Utica, New York and represented locomotive engineers working on the New York Central (Lines Eastward.) & Delaware, Lackawanna & Western. his birthplace
Little falls, New York is close to Utica, 23.2 miles to the east of Utica, which is on the New York Central's mainline between Albany, and Syracuse, New York.

Tom Brown has found some interesting information about George A. Moore showing phone directories, and census information.

That is very interesting Larry, I live in Little Falls, NY.
There are still a few Moore's in the area. There are a few Moore families in Salisbury, NY, about 5 miles northeast of Little Falls.

Edward it's interesting that you actually live in the community of Little Falls, New York, it would be nice if you could post a picture of the town. George A Moore evidently lived in Syracuse, New York, but was a member of the Brotherhood of Locomotive Engineers Division in Utica, that I see is about 55 miles west of there.

Larry