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Federated fine-tuning of Large Language Models (LLMs) is obstructed by a trilemma of challenges: protecting LLMs intellectual property (IP), ensuring client privacy, and mitigating performance loss on heterogeneous data. Existing methods like Offsite-Tuning (OT) secure the LLMs IP by having clients train only lightweight adapters, yet our analysis reveals they suffer from a fundamental performance bottleneck, leaving a significant gap compared to centralized training. To bridge this gap, we introduce FedProxy, a new federated adaptation framework. FedProxy replaces weak adapters with a unified, powerful Proxy Small Language Model (SLM), compressed from the proprietary LLM, to serve as a high-fidelity surrogate for collaborative fine-tuning. Our framework systematically resolves the trilemma through a three-stage architecture: (i) Efficient Representation via server-guided compression to create a resource-friendly proxy; (ii) Robust Optimization through an interference-mitigating aggregation strategy to handle data heterogeneity; and (iii) Effortless Fusion via a training-free "plug-in" mechanism to integrate learned knowledge back into the LLM. Experiments show FedProxy significantly outperforms OT methods and approaches centralized performance, establishing a new benchmark for secure and high-performance federated LLM adaptation.