Jackie Robinson's Last Home Run Ball

[BigJJ]

Let's think about what kind of corrobative evidence may be out there.
First i think it would be a plus to confirm that the ball you have is a Japanese professional baseball of the type used in 1956. This should be a first step. Establishing that this is a -1956- professional Japanese ball. This should be doable.
Second, are there any early photos of your Dad and the ball, either from Japan, which would be a plus, or from home many years ago.
Third, did your dad save the ticket stub and/or program.
Fourth, helpful to history, the Japanese film a tremendous amount. Perhaps there is a video of the home run, including your dads catch. This is a very real possibility. Perhaps Major League Baseball has a liaison to the Japanese professional league who might be of assistance.