In recent years, the development of online social network platforms has led to increased research efforts in social recommendation systems. Unlike traditional recommendation systems, social recommendation systems utilize both user-item interactions and user-user social relations to recommend relevant items, taking into account social homophily and social influence. Graph neural network (GNN)-based social recommendation methods have been proposed to model these item interactions and social relations effectively. However, existing GNN-based methods rely on centralized training, which raises privacy concerns and faces challenges in data collection due to regulations and privacy restrictions. Federated learning has emerged as a privacy-preserving alternative. Combining federated learning with GNN-based methods for social recommendation can leverage their respective advantages, but it also introduces new challenges: (1) existing federated recommendation systems often lack the capability to process heterogeneous data, such as user-item interactions and social relations; (2) due to the sparsity of data distributed across different clients, capturing the higher-order relationship information among users becomes challenging and is often overlooked by most federated recommendation systems. To overcome these challenges, we propose a federated social recommendation approach with enhanced hypergraph neural network (HGNN). We introduce HGNN to learn user and item embeddings in federated recommendation systems, leveraging the hypergraph structure to address the heterogeneity of data. Based on carefully crafted triangular motifs, we merge user and item nodes to construct hypergraphs on local clients, capturing specific triangular relations. Multiple HGNN channels are used to encode different categories of high-order relations, and an attention mechanism is applied to aggregate the embedded information from these channels. Our experiments on real-world social recommendation datasets demonstrate the effectiveness of the proposed approach. Extensive experiment results on three publicly available datasets validate the effectiveness of the proposed method. CCS Concepts: center dot Security and privacy; center dot Computing methodologies - Machine learning; Learning latent