The person emerging from the teleporter will be indistinguishable from the person who entered.

Just as you are indistinguishable from yourself from one moment to the next.

As such, they would claim continuity whether it was true or not.

Just like you.

they remember stepping in, but it was a copied memory.

All our memories are copies. Most of them aren't even real. 'Copied memory' is a meaningless phrase.

It doesn't matter if consciousness is physical or not.

Yeah it does.

Someone changed from alive to dead.

Who did?

This has nothing to do with cells. This is a direct question about continuity of consciousness.

Yep. He has it. So do you. Prove the difference.

You just have to imagine that instead of being teleported, you were copied and killed.

That's what time does.

It's really not that difficult to understand that a teleporter might accidentally be implemented as a copy & kill machine, and if it was, we wouldn't notice by looking at the copies.

No you would 'notice' because that is how the machine works.

You would have to know how consciousness works, which we don't, and you'd have to know that the machine is capable of preserving what needs to be preserved in order to maintain conscious continuity.

Just like every day. In order to greet your coworkers you have to know how consciousness works, which we don't, and you'd have to know that the passage of time is capable of preserving what needs to be preserved in order to maintain conscious continuity. Which we don't.

I'm sorry, but if this is a problem then it is a problem without a teleporter. The teleporter is just drapery over the problem of other consciousnesses.

I'm sorry you're having such trouble understanding this.