The last blow of the war actually took place a few weeks later

From the excellent Perilous Fight by Stephen Budiansky, an account of the naval aspects of the War of 1812. Page 362.

The last blow of the war actually took place a few weeks later, a half a world away. Master Commandant Lewis Warrington, the aggressive-minded commander of the American sloop of war Peacock, refused to believe the hail from the captain of an East India cruiser he approached June 30 near Sumatra that the war was over, and ordered him to strike his colors; when the British ship refused, he fired a broadside into her. The British commander, Lieutenant Charles Boyce, was seriously injured and had his right leg amputated two weeks later. It had been five months since the ratification of the “Treaty of Peace and Amity between His Britannic Majesty and the United States of America.”