for this example I will use Rei 2 and Rei 3. imagine you are Rei 2 and you at this moment are self aware and present you are living; we will call this your current consciousness. now imagine you die and your soul like Rei 2's is put in a new empty vessel Rei 3. will your consciousness/living/self-awareness still be the same or will the past you be actually dead;. not physicly or memory wise but continues existance will your continues existence still be there.

I could also phrase it like this imagine when you die everything goes black would you in this case still be in the world or would everything be black. would the transfer of your soul keep this existence. for you/Rei let's say you have Lillith's soul not a human one.

Required reading: https://wiki.evageeks.org/soul