With Taiwan's industries rapidly advancing towards automation and intelligence, the IIoT plays a pivotal role in enhancing factory efficiency and production management. However, the emergence of quantum computing introduces significant security challenges, particularly for data transmission and privacy protection. We introduce a novel lattice-based cryptographic authentication and key management scheme designed for the Industrial Internet of Things (IIoT) within Wireless Sensor Networks (WSNs), focusing on establishing a quantum-resistant industrial communication system. The proposed scheme utilizes Crystals-Kyber technology and is built around the Learning With Errors (LWE) problem to provide a robust foundation for security against both traditional and quantum threats. It features innovative methods to safeguard against password guessing, stolen verifier, and replay attacks, enhancing data confidentiality and system integrity. By integrating advanced cryptographic techniques resistant to quantum decryption, this research ensures the secure management and utilization of critical production data, supporting the ongoing transformation towards more intelligent manufacturing processes and sustaining global competitiveness for Taiwanese industries.