Are you certain that he came to the US? There is a record of a Henry Galligan, age 21,(b. 1886 in County Cavan, Ireland) arriving in Montreal, Canada on October 20, 1907 aboard the "Lake Manitoba". His destination is listed as Vancouver, British Columbia.
Do you have an exact date and ship's name for his emmigration? Any other clues, e.g., did he travel with his parents or any siblings?