On the same day a Florida appeals court tossed out John Connolly Jr.’s murder conviction, the actor playing the corrupt former FBI agent in “Black Mass,” the movie about Whitey Bulger, showed up on the South Boston set. Stern-faced and wearing a beige suit, Aussie actor Joel Edgerton looked reasonably like Connolly, the mob boss’s FBI handler who was convicted for his role in a scheme to murder businessman John Callahan in 1982. While cameras were rolling Wednesday on Silver Street, Florida’s Third District Court of Appeal announced it’s sending the Connolly case back to a lower court, meaning he could soon be sprung from prison. “Black Mass,” based on the book of the same name by former Globe reporters Dick Lehr and Gerry O’Neill, stars Johnny Depp as the notorious South Boston mobster. It’s being directed by Scott Cooper.