A and B are not the same, but they are “connected” via causes (hetu) and results (phala.)
One could ask why A should worry about B’s suffering if they’re not the same. My understanding is that the “momentary perception” of me/mine will still remain. In a way, the same thing happens in a single lifetime too, right? Each citta arises and passes away but the “momentary perception” of self is always there. When a toddler grows into an adult human, it becomes a totally different person but there is a continuity (since it is the same life stream) which is why when a human thinks about their past, there is the perception that it is the same person.