Apparently the British took one of those cartridges as the starting point for the .303, but as I noted below, it's EXTREMELY unlikely that they ever discussed that fact with him.
If I recall the account I read, Rubin developed the original round ca. 1882. It is referred to as the ".303 Rubin" in various references, and a picture is included in Skennerton's book on Lee Enfields.
Whether the British Small Arms Committee consulted with Rubin regarding this round is somewhat obscure, but I would be willing to bet that it was tested by the Brits with his full knowledge and cooperation.
At any rate, the original .303 round was a black powder affair, later modified for use with the then-new smokeless Cordite. In 1888, it was cutting edge technology and gave good service for decades, much to the chagrin of its detractors, and will continue to do so for decades to come.
The .303, in addition, has probably killed more varieties of game than any other cartridge, and is still used as a military round in some third and fourth world countries today. Lee-Enfield rifles continued to be produced in .303 well into the 1980s in India, as well. (Mine is dated "1986.")
Furthermore, Lee bolt action rifles in .45-70 were officially adopted by both the U.S. Army and Navy as the Models 1882 and 1885 respectively, later followed by the 1895 Lee 6mm Navy straight pull rifle, many of which were on board the U.S.S. Maine when it was sunk in Havana Harbor in 1898.