Reliability management in cloud service systems is challenging due to the cascading effect of failures. Error wrapping, a practice prevalent in modern microservice development, enriches errors with context at each layer of the function call stack, constructing an error chain that describes a failure from its technical origin to its business impact. However, this also presents a significant traceability problem when recovering the complete error propagation path from the final log message back to its source. Existing approaches are ineffective at addressing this problem. To fill this gap, we present ErrorPrism in this work for automated reconstruction of error propagation paths in production microservice systems. ErrorPrism performs static analysis on service code repositories to build a function call graph and map log strings to relevant candidate functions. This significantly reduces the path search space for subsequent analysis. Then, ErrorPrism employs an LLM agent to perform an iterative backward search to accurately reconstruct the complete, multi-hop error path. Evaluated on 67 production microservices at ByteDance, ErrorPrism achieves 97.0% accuracy in reconstructing paths for 102 real-world errors, outperforming existing static analysis and LLM-based approaches. ErrorPrism provides an effective and practical tool for root cause analysis in industrial microservice systems.