Wikipedia pages of Superman II and Richard Donner both show that Richard Donner had directed Superman II along with Richard Lester, but he was uncredited.
Well, if he was uncredited, how can anyone credibly say that he was involved in the direction of the movie? What are the sources?
There is no controversy about the main facts of what happened with Richard Donner in the filming of Superman II. He was fired by Alexander and Ilya Salkind, the brothers who were producing the film. Filming on the sequel had started before the release of Superman, but there was a break in the fall of 1978, so that Donner (who was originally intended to completely direct both features) could finish the post-production work on the first film. Due to several conflicts, after Superman was released, the Salkinds decided not to bring Donner back to finish making Superman II.
However, Richard Donner had already directed so much of the movie that there was not enough footage remaining to be shot for Richard Lester to simply finish it and be credited as the director. (The credited director has to have overseen at least half the shooting, according the Directors' Guild rules.) So Lester actually went back and reshot enough material to put his contribution over half. In order to save money, they tried to reshoot things that could be done inexpensively. So Lester re-filmed a lot of close shots, which didn't require reconstituting whole sets. You can actually see this if you look for in in the theatrical cut of the film. In many cases, close-up response shots show the actors looking subtly different than they do in longer shots. The reason is that the two scenes were filmed by the two different directors weeks or months apart, making it hard to duplicate characters' "looks" precisely.
For his work, a lot of which remained in the Superman II (Gene Hackman, in particular, refused to reshoot things with Lester, so virtually everything with Lex Luthor was either filmed by Donner or used a double) Donner could have received a credit, just not as the film's director. However, I believe that he decided to forgo any credit, not wanting to be further associated with what he felt was a botch-up of his work.
Eventually, after the rights to Superman II had passed around for a while, Donner did put together something approximating his original planned cut of the film in 2006. Superman II: The Richard Donner Cut used a substantial amount of footage that Donner had shot that had not made it into the final film, supplemented by some of Lester's scenes, and even some screen tests where final footage was not available. (Reshooting scenes was generally not possible, given the long time that had elapsed since the original project and Christopher Reeve's paralysis, leading to his death in 2004.)
