If person A tells person B a message, person B then gets this message, understands it and remembers what he understood of it. But we cannot say that this message was physically transferred from A to B. All that was physically transferred were movements of air molecules as sound waves. The message was conceptually transferred and not physically transferred. The message is a conceptual entity and not a physical entity. We also cannot say that the message that B had and the message that A had are exactly identical, because B might have understood the message slightly differently. Also, we are able to trace the history of the transmission of the message, for e.g. from A to B to C etc.
Also, similar is the transfer of a flame from one candle to another. Physically, the heat from one burning candle ignited another candle's wick, causing it to start burning. But we cannot say that the flame itself transferred from one candle to another. The flame here as something that moves from one candle to another is again a conceptual entity and not a physical entity. We created the concept of the flame. In physics, it's simply plasma emitting from a burning wick. As the candle burns, the plasma ions get replaced. There is no single physical entity as the flame. The flame from one candle is also not identical to the flame of another candle that it ignited. We can also trace the history of transmission of the flame from one candle to another. So, the transfer of the flame from one candle to another is also a conceptual transfer and not a physical transfer.
So too is "rebirth" in Buddhism. It's not a physical rebirth or physical transfer, but a conceptual rebirth or conceptual transfer. Similarly what a "being" or "person" or "self" is, are also concepts. If person C is reborn and now becomes person D, person D and person C are not exactly the same, yet not completely different, just like the message that transferred from A to B. And it is possible through attainments of meditation, to trace the history of transmission from C to D.
Instead of using the term "rebirth", I prefer to say that suffering or dukkha continues beyond physical death, and that suffering or dukkha is only ended by Nibbana, and not ended by physical death.