Edge computing facilitates low-latency and high-bandwidth services by deploying edge servers close to data sources and end users. However, dynamic edge environments, characterized by fluctuating resources and user mobility, etc., necessitate efficient service migration to maintain consistently low latency. Traditional migration methods incur significant latency due to redundant data transfers, especially in containerized environments where shareable storage layers and redundant files across non-shareable layers in Docker containers exacerbate inefficiencies. Despite advances in layer sharing migration techniques, the challenges remain as follows: (i) shareable layers are limited due to coarse granularity, and (ii) approximately 97% of files across layers are duplicates. To solve this problem, we propose a framework for live migration of Docker containers, minimizing file system transfer size through file-level storage sharing and enhanced layer reuse. Our method reuses identical image layers and shares files both across layers and with those already present on the target server, transferring only the necessary files. Experimental results demonstrate that our file-level storage sharing strategy outperforms state-of-the-art techniques in terms of reducing the migration time of Docker containers.