According to Osho, asking if there is a soul misses the point: there is no fixed, unchanging entity; what continues is a flowing continuity—a stream of consciousness and tendencies—changing every moment. Identity is a process, not a thing. Resting as witnessing awareness reveals the flux without clinging to an essence; thus transmigration is continuity, not a permanent soul-substance.
There isn’t a hard, unchanging “me”; there’s a moving stream you can watch.