It's similar to the objection being made that the other being isn't you, in the same sense a fully-replaced ship is no longer the same ship. Except it is, because there's continuity. For a vessel it's the continuity of identification; for an individual it's the appearance of continuity of consciousness, which is philosophically no different from actual continuity of consciousness.
There is no "from your perspective" of the dead original, because they're dead and their perspective ceases at the exact moment the new perspective resumes. The only way perspective can continue is in the case of the copying variant, which simply produces two "yous" that diverge immediately into two distinct individuals who share the same history.
In the case of the transportation instead of duplication, "you" continue to exist without noticing any difference. The appearance of continuity is impossible to notice, only to rationalize intellectually. It is true that the individual biological construct that is your original goes in and dies, but that doesn't matter. "You" are your consciousness. If you suffered irreversible amnesia, you wouldn't be "you" anymore; the loss of your consciousness is functionally equivalent to death. But if you woke up one day in a robot body, you'd probably argue that you were "still you," even though clearly something happened to your biological body. You can replace what constitutes you as long as your consciousness believes it remains the same.
After all, there's no way to know you weren't created by a duplication process this morning that destroyed the body that went to sleep in your best last night. There's no way to know the universe existed five minutes ago. "You" are perception and consciousness, and as long as a "you"
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