IF we grant that teleportation is possible and on the other side comes out someone with your exact DNA, memories, etc, couldn't it be possible for the consciousness to be transmited?
Known Space shows that the teleporter does indeed kill the original and make a copy at the destination. If I recall right it either was revealed in an accident/malfunction where the original wasnt killed. Or more likely some criminal was using it to be in 2 places at once to commit some crime. The Puppeteers confirm this and that there is no soul or afterlife. Which makes their casual use of the teleporter all the more baffling considering their intense fear of death or injury.
TNG though played very loosy goosy with the teleporters.
Funny I have read Ringworld (All 4 novels) several times and don't recall that.
Omega said it came up in the Gil Hamilton of ARM stories. Which is possible -- the ARM is all about suppressing technologies that are too dangerous for the public to know about, so most of the stories read like secret histories or conspiracy theories, which subvert established elements of the setting.
But I don't remember it coming up there, either. And even if it did, it's from an early period in both the the development and internal chronology of Known Space. Rather than being suppressed, teleporters are so ubiquitous by the time of Ringworld. The first novel starts with the protagonist teleporting around the world to extend his birthday. It's everyday technology, and humanity of the time is far more technologically advanced than in the time of Gil Hamilton. So you'd think the truth would have come out. Not only that, but the first major stop in Ringworld is the Puppeteer homeworld, where teleportation is even more advanced. And the Puppeteers are smarter than humans, even more advanced, and terrified of injury or death, but still use the technology. So even if there's a Gil story that says teleportation is death, it's never referenced again, and it's clearly contradicted by the main events of Known Space. So even in the best case, it's a random idea that was dropped like a stone.