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With the widespread deployment of basic models in edge intelligence, communication bandwidth has become a core bottleneck restricting the scalability of federated learning. Although one-shot federated learning alleviates this problem by minimizing communication rounds, existing iterative fine-tuning or knowledge distillation methods still face challenges such as high server-side computational costs and hyperparameter sensitivity. Analytical federated learning achieves efficient gradientfree aggregation using least-squares closed-form solutions, but in environments with non-independent and identically distributed data, its static feature assumptions fail, leading to feature manifold misalignment and severely impairing model performance. To address this contradiction, this paper proposes the FedOPAL framework. This framework adapts the visual prompts as feature rectifiers, actively correcting the feature distribution of heterogeneous data to a linearly separable space by applying local proximal constraints, thereby satisfying the theoretical assumptions of analytical federated learning. Experimental results show that FedOPAL not only significantly outperforms the original analytical methods on several benchmarks, but also achieves accuracy comparable to state-of-the-art iterative methods while maintaining zero server-side training costs, providing a new engineering paradigm for efficient collaboration of large models on the edge.