What if it didn't destroy the old one? Would there be any doubt at all?
Does it make a difference if it's a teleporter that destroys the original as an necessary part of its function, vs one that destroyed the original but didn't need to do so, vs one that did not destroy the original?
I would hope that any working 'teletransporter' would provide a near-enough-perfect replica?
By any external measure the replica could be functionally and physically identical to the original, but so long as new matter is used it would still be a replica.