While Quantum entanglement theory is a treasure trove for fiction writers it is, like so much of Einstein's work, untestable.The first point I'd make is that the theory does not propose the transference of particles but of quantum states. And while the theory suggests that if two atoms have at some time been in contact and are therefore "entangled" an action affecting one will affect the other instantly even if they are now at opposite ends of thee universe.
Which is fine in theory but if I remember correctly the 1993 experiment when one attom was excited by an electro - magnetic charge, another one on the other side of the laboratory also became excited. ( I believe that since then quantum states have been transferred over distances of several hundred kilometers, but that's still a long way short of a few thousand light years. But those experiments use atoms of a particular kind. There is lots of different stuff in a human:
THE MAKING OF A MAN, a folk poem turned into a song by Steeleye Span
Iron enough to make a nail,
Lime enough to paint a wall,
Water enough to drown a dog,
Sulphur enough to stop the fleas,
Potash enough to wash a shirt,
Gold enough to buy a bean,
Silver enough to coat a pin,
Lead enough to ballast a bird,
Phosphor enough to light the town,
Poison enough to kill a cow,
The problem, once you had put all those ingedients together would be to write the quantum states onto the roght atoms in the right order. Sorry, but there is no chance of achiving physical teleportation. But if you think of other, non physical, states of being then Teleporation Travel Inc. could be in business.