To address unfairness issues in federated learning (FL), contemporary approaches typically use frequent model parameter updates and transmissions between the clients and server. In such a process, client-specific information (e.g., local dataset size or data-related fairness metrics) must be sent to the server to compute, e.g., aggregation weights. All of this results in high transmission costs and the potential leakage of client information. As an alternative, we propose a strategy that promotes fair predictions across clients without the need to pass information between the clients and server iteratively and prevents client data leakage. For each client, we first use their local dataset to obtain a synthetic dataset by solving a bilevel optimization problem that addresses unfairness concerns during the learning process. We then pass each client's synthetic dataset to the server, the collection of which is used to train the server model using conventional machine learning techniques (that do not take fairness metrics into account). Thus, we eliminate the need to handle fairness-specific aggregation weights while preserving client privacy. Our approach requires only a single communication between the clients and the server, thus making it computationally cost-effective, able to maintain privacy, and able to ensuring fairness. We present empirical evidence to demonstrate the advantages of our approach. The results illustrate that our method effectively uses synthetic data as a means to mitigate unfairness and preserve client privacy.