War Hawks, in the history, are composed of young Southerners and Westerners which were elected in 1810 to the US Congress. They met from 1811 to 1813 to discuss matters about expansion of the United States. With their great ambition to take hold of the territories in the Northwest and in Florida, they were engaged in war with Great Britain.
Hence, the answer to the item is FALSE since at this time, it was Great Britain who were in position of the territory.