There are a few problems with this idea, unfortunately. One is that it
would be a violation of the theory of relativity to have a teleportation
device which sent information or people with an effective speed > c.
Even if you could do this, photons leave earth in all directions,
spreading out and becoming thinly scattered. Once you get far enough
from the earth to be seeing a considerable distance into the past, the
chance that a photon from earth will actually be heading your way is
very small. So the amount of information you can gather from a single
vantage point is limited. You could get around this by having a large
number of observers positioned to catch many of the photons.
Even without FTL travel, the idea could conceivably work. Imagine if there
were a giant mirror in space, which reflected light back towards earth.
Then you could look in the mirror and see what was happening on earth in
the past. Unfortunately there are no such mirrors, but still there is
matter which absorbs and re-emits photons. Conceivably with enough
computing power it might be possible to analyze the state of gas clouds
and other matter and determine what photons had fallen on them in the past.
This gets into Tipler's idea that a super-intelligence in the future will
be able to put together all the clues it finds in its environment and do
a good job of reconstructing the past, to the point where it can, as you
say, give past individuals rebirth.
Hal