Cloud-based data sharing systems (DSS) have become prevalent due to their ample storage and convenient access control. To protect sensitive data privacy in DSS, anonymous identity-based encryption (IBE) is a promising approach, enabling encryption using a recipient’s identity as a public key, while preventing identity and data leaks out of ciphertexts. As complete anonymity risks abuse and illegal usage, Blazy et al. introduced the notion called anonymous IBE with traceable identities (AIBET) at ARES’19, allowing users with tracing keys to identify recipients from ciphertexts. Unfortunately, existing AIBET schemes lack tracing key delegation and only consider security in weaker models (i.e., selective-identity attacks and chosen-plaintext attacks), posing risks of inconvenience and user privacy leaks. In this paper, we introduce a novel notion called anonymous hierarchical identity-based encryption with delegated traceability (AHIBEDT) for DSS. We formalize its syntax and define security notions in stronger models (i.e., adaptive-identity attacks and chosen-ciphertext attacks). In addition, we demonstrate that a concrete AHIBEDT scheme can be simply obtained from a hierarchical IBE scheme and a one-time signature scheme. The comparison results indicate that, despite a substantial increase in communication and computational costs, our approach achieves better security and functionality.