It is a difficult question. First of all, if the original person is not destroyed before their clone is reconstructed at the receiving end, they are not the same person anymore. Any overlap conscious existence immediately renders them different people. The clone would have the memory of arriving at the destination, the original would not. They diverge from that moment onward.
If the process physically destroys the original prior to the construction of the clone, it's harder to say. The clone would have the conscious memory of the original and would likely regard him/herself as the same person, despite the obvious interruption of physical existence.
A persons identity is strongly bound to their past experiences, which in turn exists only as memory for that individual. If you think about it, when you woke up this morning, your sole connection to the past is only a memory. You have no conscious recollection of the intervening time asleep. So, from that perspective, a teleported person has a sense of continuity that we are likely comfortable with.
However, you do have the additional knowledge that your body is the same one that got into bed and went to sleep. I would suggest that this knowledge, often overlooked, is also subliminally fundamental to our sense of continuity. A person teleporting according to your proposed method, fully aware of the way in which it operates, would not have this reassurance.
In my opinion, a clone, no matter how perfect, is not the original entity. Without continuity of their physical and mental existence, they would cease to be the same individual.
Worse still, I would imagine the cloned entity would eventually develop some form of neuroses deriving from the knowledge of the destruction of their original self.
