Non-negative matrix factorization (NMF) with missing-value completion is a well-known effective Collaborative Filtering (CF) method used to provide personalized user recommendations. However, traditional CF relies on a privacy-invasive collection of user data to build a central recommender model. One-shot federated learning has recently emerged as a method to mitigate the privacy problem while addressing the traditional communication bottleneck of federated learning. In this paper, we present the first one-shot federated CF implementation, named One-FedCF, for groups of users or collaborating organizations. In our solution, the clients first apply local CF in-parallel to build distinct, client-specific recommenders. Then, the privacy-preserving local item patterns and biases from each client are shared with the processor to perform joint factorization in order to extract the global item patterns. Extracted patterns are then aggregated to each client to build the local models via knowledge distillation. In our experiments, we demonstrate the feasibility of our approach with two MovieLens datasets. One-FedCF can obtain results competitive with the state-of-the-art federated recommender systems at a substantial decrease in the number of communications.