In the Army Special Services, he was involved in entertaining troops in Europe and England, which included a "Tribute to Gershwin" concert with the Stuttgart Symphony Orchestra in Germany.
After his Army duty, Cuesta toured the United States and Canada and developed his own highly personal style.
While living in Toronto, Cuesta and his group became popular for visiting musicians, including Benny Goodman on one occasion.
Cuesta made countless personal appearances performing and conducting in jazz festivals, state and county fairs, conventions, supper clubs, and symphony pops concerts.
His only son, Henry, Jr., was shot and killed in a robbery at the age of seventeen while he was working in 1987 at a movie theater on Wilshire Boulevard in Santa Monica, California.