Sorry, but your friend's button find is not from the Revolutionary War era. It is definitely the 1902-to-1952 version of a British Army "general service" uniform button. You can verify that info in the buttons section at the very-scholarly UKDFD website (United Kingdom Detector Finds Database). A less scholarly site, the Colchester Treasure Hunters metal-detecting club in Britain, has the same time-dating for that button (with many photos) here:
Militarynamedregs
To view several exact matches for your friend's button (with time-dating), scroll down past the British Artillery buttons to the British Army ones.