Threshold sharing schemes provide fundamental building blocks for secure distributed computation and the safeguarding of secrets. Since its invention, many enhancements to threshold secret sharing have been proposed. Proactive Secret Sharing, for example, provide enhanced protection by updating the shares periodically in a distributed fashion. Traditionally, PSS schemes retain the same set of shareholders and the same access structure across updates. A more general problem is the redistribution of shares between different (possibly disjoint sets of) shareholders and different access structures. We study this generalization and present a new protocol that performs verifiable secret redistribution between arbitrary shareholders and across arbitrary access structures. We also identify a vulnerability in the previous protocols that allows faulty shareholders to distribute invalid shares to new shareholders, and we prove the security of our scheme with an information-theoretic security proof.