Act IV or Act V
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Hamlet's inner conflict is truly only resolved at the end of the play, as he is dying. He realizes that his mother was not involved in his father's death, kills Claudius as revenge for the murder of his father, makes peace with Laertes, noting that neither one of them is truly at fault for what has happened between them, and asks Horatio to "report my cause aright" to those who question what has happened.
While it might be difficult to believe, Hamlet's inner conflict is only resolved when he comes to the end of his journey to avenge his father's murder. Since the murder is secret to everyone except Hamlet, the ghost, Horatio, and Claudius, Hamlet cannot feel truly free until he believes all members of the court will, in fact, know the truth and carry on in the future knowing how the reign of Hamlet's father ended. Horatio, although he wishes he could kill himself, is assigned to carry on in Hamlet's place and is expected to do the job which Hamlet can no longer do. However, we believe that Hamlet is now at peace.