Knowledge Distillation (KD) accelerates training of large language models (LLMs) but poses intellectual property protection and LLM diversity risks. Existing KD detection methods based on self-identity or output similarity can be easily evaded through prompt engineering. We present a KD detection framework effective in both white-box and black-box settings by exploiting an overlooked signal: the transfer of MoE "structural habits", especially internal routing patterns. Our approach analyzes how different experts specialize and collaborate across various inputs, creating distinctive fingerprints that persist through the distillation process. To extend beyond the white-box setup and MoE architectures, we further propose Shadow-MoE, a black-box method that constructs proxy MoE representations via auxiliary distillation to compare these patterns between arbitrary model pairs. We establish a comprehensive, reproducible benchmark that offers diverse distilled checkpoints and an extensible framework to facilitate future research. Extensive experiments demonstrate >94% detection accuracy across various scenarios and strong robustness to prompt-based evasion, outperforming existing baselines while highlighting the structural habits transfer in LLMs.