This paper proposes a collaborative learning framework based on vertical federated learning for detecting false data injection attacks in distribution networks. The proposed framework empowers entities that are responsible for a sub-network to collaboratively construct an FDIA detection model, effectively addressing issues associated with data sharing and enabling the utilization of various measurements from each sub-network. The proposed framework enables real-time collaboration between the server and the grid edge-side by allocating the two models created through the split learning approach applied to the proposed attention-based hybrid deep learning model. The grid edge-side is tasked with extracting spatial features, while the server is responsible for extracting temporal features from the data processed by the grid edge-side. The edge-side model is designed by adopting an attention module integrated into a deep learning model while the server-side model is designed based on the Bi-LSTM model. The effectiveness of the proposed framework is demonstrated on the IEEE 123 and IEEE 37 node test systems.