During the War of 1812, Conway was commissioned as an
Ensign in the
United States Navy, and was promoted to
Lieutenant in 1813. In 1817, Conway became a clerk in the
U.S. Treasury. Having saved money for his journey, the following year he joined the migration West to the
Missouri Territory. In 1820, he moved to the Arkansas Territory. There he became active in territorial politics, forming a friendship and an alliance with Robert Crittenden. His younger brothers
James S. and
Elias N. Conway also later became politicians in Arkansas after it became a state in 1836; they served as first and fifth governors of the state, respectively. In Arkansas Territory, he was appointed as receiver of public moneys, serving from 1820 through 1821. Conway was elected in 1822 as a territorial delegate to the
Eighteenth Congress and was re-elected to the
Nineteenth, and
Twentieth Congresses, serving in total from March 4, 1823 until his death. Following political differences in 1825, Conway and Crittenden grew apart, publicizing their feud in newspapers. ==Death and legacy==