teleportation machine

Suppose there is a teleportation machine that works in the following way:

The teleporter scans your body and makes an accurate, detailed log of precisely all of your atoms and subatomic particles: the entire and exact quantity, where they are in your body, and how they are arranged relative to each other. This includes all of your cells.

The teleporter incinerates your body into dust.

In a remote location, the teleporter takes the detailed log of you and all of your particles, and with a fresh new supply of the same kind of particles (atoms, etc.) creates a body exactly like yours in exact and precise accordance with the log.

Your friend steps into the teleporter in Los Angeles and then is teleported to Berlin. She steps out of the teleporter with all of the same memories (because the brain was created exactly the way it was left back in Los Angeles). She says “Wow, I can’t believe I’m in Berlin! I was just in Los Angeles and now I’m in Berlin. You have to try this It’s incredible!”

Suppose there is absolutely no room for error in steps 1 and 3 above. (Just assume it for the sake of discussion). Is the person in Berlin the same person that stepped into the teleporter in Los Angeles? Would you step into the teleporter? Explain your answer.