To expand on this, all that we really have is a feeling of self-awareness, and a memory of a continuous series of events leading up to this moment. Both teleporter clones would have the same subjective-I feeling, and the memories. Which one is "real" is a meaningless distinction.
It's like how I woke up this morning, and I have the memory of going to bed last night, but I am no longer that person who went to bed; I cannot know his mind other than in the memories that I have. Did my consciousness in this moment come from him? Clearly not! If he was conscious (which I cannot actually prove now), there was a gap of many hours. (Actually, neuroscience tells us our consciousness dips out every ~90 seconds, so our brains can attend to other tasks. As a 'fun' experiement, try to wait out an itch without scratching it, and pinpoint the moment it goes away. Or just have ADHD.)
Same thing with the transporter clones. Each would "come to" in the moment, with the illusion of continuous, conscious experience. The original would be just as "dead" as the me that went to sleep last night.