Recommender systems (RSs) are essential for the modern web, providing personalized suggestions that alleviate information overload and enhance the user experience across various platforms. Graph neural networks (GNNs) have been proposed for RS and demonstrate significant potential. However, GNN-based methods are prone to oversmoothing in practical settings, limiting their expressive power and ability to capture complex data patterns effectively. Recent research has also explored graph-transformer-based RS methods that, while improving performance, tend to increase computational costs, particularly in large-scale scenarios. To address these challenges, we introduce FAHMRec, an efficient hypergraph-based model for multi-behaviour recommendation. Experimental results demonstrate that our method outperforms state-of-the-art baselines in recommendation quality while also reducing memory and time costs.