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Federated Learning (FL) is a distributed machine learning framework in which a set of local communities collaboratively learn a shared global model while retaining all training data locally within each community. Two notions of fairness have recently emerged as important issues for federated learning: group fairness and community fairness. Group fairness requires that a model's decisions do not favor any particular group based on a set of legally protected attributes such as race or gender. Community fairness requires that global models exhibit similar levels of performance (accuracy) across all collaborating communities. Both fairness concepts can coexist within an FL framework, but the existing literature has focused on either one concept or the other. This paper proposes and analyzes a post-processing fair federated learning (FFL) framework called post-FFL. Post-FFL uses a linear program to simultaneously enforce group and community fairness while maximizing the utility of the global model. Because Post-FFL is a post-processing approach, it can be used with existing FL training pipelines whose convergence properties are well understood. This paper uses post-FFL on real-world datasets to mimic how hospital networks, for example, use federated learning to deliver community health care. Theoretical results bound the accuracy lost when post-FFL enforces both notion of fairness. Experimental results illustrate that post-FFL simultaneously improves both group and community fairness in FL. Moreover, post-FFL outperforms the existing in-processing fair federated learning in terms of improving both notions of fairness, communication efficiency and computation cost.