We can start with some science fiction. Here on Earth, I enter the Teletransporter . When I press some button, a machine destroys my body, while recording the exact states of all my cells. This information is sent by radio to Mars, where another machine makes, out of organic materials, a perfect copy of my body. The person who wakes up on Mars seems to remember living my life up to the moment when I pressed the button, and is in every other way just like me.
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Derek Parfit (2012) studied this question.
Synapse has enriched 3 closely related papers on similar clinical questions. Consider them for comparative context: