Keep in mind that British muskets surrendered at Yorktown and other places as well as those taken by other means were cleaned, repaired when necessary, and issued to US regulars along with French muskets after the Revolution during the early days of the American republic. Those not needed for issue, both British and French, were kept in storage at various arsenals including Springfield as well as others. The entire US Army was not issued French muskets or the early made US copies thereof until the time of the War of 1812. Militia continued to be issued British flint muskets as late as 1861.
For good information read
U.S. Military Flintlock Muskets, and Their Bayonets, the Early Years, 1790-1815 by Peter A. Schmidt as well as
American Military Shoulder Arms: From the 1790s to the End of the Flintlock Period: Vol 2 by George D. Moller.
For information on the issue of British
flint muskets to some companies of the Virginia state militia in 1861 - especially those of the less than reliably loyal western counties - at the beginning of the American Civil War, see "Message from the Execttive of the Commonwealth,
with Accompanying Documents, Showing the Military and Naval Preparations for the Defence of the State of Virginia" at:
http://docsouth.unc.edu/imls/message/message.html
The Brown Bess served on for almost 80 years in American hands after the end of the American Revolution.