I had forgot to mention that the cartridges contained a 217 gr. lead bullet which, according to the catalogs, was used by U.M.C. in the 44-40 from 1887-1904.
The cartridge illustrations in the 1889 & 1896 catalogs do show the S H designation in some of the head stamps.
The next U.M.C. catalog to show cartridge illustrations is the 1905 which indicates that the S H designation has been eliminated.
So it appears that likely the S H moniker appeared before 1889 and was discontinued sometime between 1897 and 1905.
I do also have some U.M.C. .44-40 head stamped cartridges that contain the same 217 gr bullet so I wonder if they were made between 1897 and 1904 or did U.M.C. use that and the S H .44 C.F. during portions of that period between 1897-1904 or earlier… (?).