Audit trails are more and more seen as a key to healthcare compliance, and it is now essential that those audit trails are confidential, verifiable and quantum-resistant. This study presents a module-lattice signature hash-chain linking authenticated encryption and trusted time-stamping based audit framework that is secure against attacks in the post-quantum era. All the clinical events are coded, signed, time-stamped and linked to the previous events, which allows for identification of tamper, event provenance and accountable access. The formal security is guaranteed by probability spaces for unforgeability, collision resistance, confidentiality and forward integrity with respect to quantum adversaries. Experimental comparison with classical based audit schemes using RSA and elliptic curve indicate a verification accuracy of 98.7%, 29.6% less storage overhead and 37.4% faster batch validation when compared to a lattice-based baseline design. The framework offers a flexible approach to the preservation of evidence about eHRs, regulatory audits, medico-legal cases, and more, and it can adapt to healthcare interoperability and compliance needs in the long term.