Answer: Hamlet did kill him while he prayed, for he believed this would allow the foul king to go to Heaven, while his father would be doomed to walk the earth as a Spirit for some period of time.
Hamlet refuses to kill Claudius during prayer because he believed that Claudius would get a heavenly afterlife after being pardoned from his sins. In this time, a person was most pure after praying because of the washing away of their sins, but Claudius was admitting his wrongdoings and murderous ways meaning his soul wasn't pure anyways.
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