The spread of fake news on social media poses a serious threat to public trust and societal stability. While propagation-based methods improve fake news detection by modeling how information spreads, they often suffer from incomplete propagation data. Recent work leverages large language models (LLMs) to generate synthetic propagation, but typically overlooks the structural patterns of real-world discussions. In this paper, we propose a novel structure-aware synthetic propagation enhanced detection (StruSP) framework to fully capture structural dynamics from real propagation. It enables LLMs to generate realistic and structurally consistent propagation for better detection. StruSP explicitly aligns synthetic propagation with real-world propagation in both semantic and structural dimensions. Besides, we also design a new bidirectional evolutionary propagation (BEP) learning strategy to better align LLMs with structural patterns of propagation in the real world via structure-aware hybrid sampling and masked propagation modeling objective. Experiments on three public datasets demonstrate that StruSP significantly improves fake news detection performance in various practical detection scenarios. Further analysis indicates that BEP enables the LLM to generate more realistic and diverse propagation semantically and structurally.