How does Hamlet and refusal kill Claudius while he is praying relate back to what the Ghost said about circumstances of his own death in Act 1 Scene 5?

Hamlet does not kill Claudius while Claudius is praying. Claudius is praying in Act III, Scene III. Hamlet decides not to kill Claudius in this moment because he believes it would be sending Claudius to Heaven, Hamlet wants Claudius to go to hell for his sins, so Hamlet decides to wait for a more opportune moment.

In Act I, Scene V the Ghost tells Hamlet that Claudius killed him "in the postern of my sleep" - while he was taking an afternoon nap. Therefore, Hamlet feels it would be fitting if Claudius meets his end in a similarly unguarded moment.