As far as I can make out:

1. there is no scientific evidence for rebirth

2. people claiming to remember past lives have vivid imaginations but no insight into what they really are

3. people claiming to remember past lives all seem to have been Julius Caesar's general, Genghis Khan's uncle or Cleopatra's maid

4. if consciousness is boundless and limitless and that in which all manifests then each individual life appears in that unbounded space, may or may not have a false sense of self whilst "alive" and then disappears back into it without affecting consciousness a jot.

Maybe the energy from one "life" can somehow set up the basis for another life, a bit like the way a sinusoidal wave goes to a zero point but with the potential to recreate a new wave based on what had just occurred. Yet each wave is entirely independent. The preservation of personal identity is the pipe dream of many a religion.

But then what do I know - absolutely nothing :d