How did hamlet escape the trap that claudius set for him?

Hamlet escaped Claudius's trap by cleverly altering the contents of the letters that were to be sent to England, which originally ordered Hamlet's execution. He substituted his own name with that of Rosencrantz and Guildenstern, leading to their deaths instead. This quick thinking allowed him to return to Denmark and confront Claudius, turning the tables on his uncle's plot against him.