I believe that the Mr. Hopkinson being referred to in this letter is Joseph Hopkinson. He served as President of the Pennsylvania Academy of Fine Arts (PAFA) from 1813 until his death in 1842. More information about the history of the PAFA is available here.
Department of War,
20th Decem. 1816
As great delay has taken place in expecting the
resolution of congress, directing the President to present gold
medals to yourself and other officers, I have thought proper
to enclose a late correspondence with Mr. Hopkinson, which
will in some measure account for that delay.
I have the honor to be,
With great respect,
Your Ob. Servt.
From Gen. Graham
enclosing correspondence with
Mr. Hopkinson. Pres. of the
Academy of Fine Arts
20th Dec. 1816