The Industrial Internet of Things (IIoT) covers a wide range of use cases with different requirements. Among them, critical use case are distinguished by their need for extremely low latency and high reliability. Similarly, 5G networks are designed to support diverse use cases that meet the requirements of IIoT applications. However, achieving ultra-low latency remains a challenge. On the other hand, the Static Context Header Compression (SCHC) mechanism, designed to address the issue of large protocol overhead in IoT, has demonstrated its effectiveness in reducing latency by compressing the packet header across various LPWAN technologies. Consequently, integrating SCHC into 5G networks will enhance the low-latency capabilities necessary to effectively support these critical IIoT use cases. This paper proposes an integration architecture of SCHC compression mechanisms within the 5G core network. Based on 3GPP specifications, the proposed solution ensures compatibility with existing 5G standards while optimizing communication efficiency and reducing protocol overhead for IIoT applications in 5G networks.