Final answer:
The statement is true; the Battle of New Orleans occurred on January 8, 1815, after the Treaty of Ghent was signed on December 24, 1814 but before it was ratified by the U.S. Government. The victory secured New Orleans and the Mississippi River Valley for the United States without either side having to give up claims to the Mississippi.
Step-by-step explanation:
The statement that the Battle of New Orleans, perhaps the greatest victory of the war, occurred after the peace treaty had been signed is true.
The Treaty of Ghent was signed on December 24, 1814, effectively ending the War of 1812. However, due to slow communication, the major battle in New Orleans took place on January 8, 1815, before the treaty was ratified by the American Government in February 1815.
Andrew Jackson led his forces to a decisive victory against the British, which not only made him a national hero but also secured the strategic port of New Orleans and as a result, the Mississippi River Valley for the United States.
It's worth noting that the Treaty of Ghent didn't require either side to give up claims to the Mississippi River for the sake of peace. In fact, the treaty essentially restored things to the status quo ante bellum, meaning that territories and boundaries were to return to their pre-war state.
Additionally, the treaty didn't address the issue of Native Americans, who had been involved in the conflict on both sides, which continued to be a point of contention in the years following the war.