Henry Shaw (Sr.) was a powerful 1920s media titan based in New York (WFT).
Henry Shaw Sr. witnessed some of the events that were important to Newt Scamander's adventures in WFT. His son Langdon told him about magic causing destruction in the city and introduced him to the Barebones, although Shaw Senior dismissed all this. Later he saw his elder son, Henry Shaw Jr., killed by Credence Barebone's obscurus. Finally, Shaw was part of the crowd watching the forcefield around the subway station.
Shaw's elder son was U.S. senator Henry Shaw Jr. Shaw Senior was very supportive of his elder son's political career; he advised his son on campaign strategy and used his newspapers to help him (WFT).
Shaw also had a younger son, Langdon Shaw (WFT).
Other canon notes and references
Shaw had an assistant called Barker (WFT).
Shaw's office was an impressive penthouse in Shaw Tower (WFT).