According to Osho, what we call ‘soul’ isn’t a fixed entity but a flowing process—a stream of moment-to-moment flames, like a lamp whose light keeps renewing. Continuity exists without an identical self: each moment is progeny of the previous. Reincarnation, then, is the ongoing flow taking new forms, not the migration of a permanent person; remembrance is not required for continuity.
There isn’t a tiny unchanging “me” that jumps bodies; there’s just a river of change that keeps going and taking new shapes.