Why is hamlet so concerned that horatio stay alive to tell his story

Hamlet wants Horatio to tell everyone his story is that the only people who know that Claudius killed the former king are Hamlet, the Queen, and Horatio. Hamlet wants everyone in Denmark to know that Claudius was a murderer who obtained the crown through illegitimate means.

I don't know how accurate I am but I wanna say the answer is Tom Robinson is more present throughout the film