Wireless Sensor Networks (WSNs) are a cutting-edge domain in the field of intelligent sensing. Due to sensor failures and energy-saving strategies, the collected data often have massive missing data, hindering subsequent analysis and decision-making. Although Latent Factor Learning (LFL) has been proven effective in recovering missing data, it fails to sufficiently consider data privacy protection. To address this issue, this paper innovatively proposes a federated latent factor learning (FLFL) based spatial signal recovery (SSR) model, named FLFL-SSR. Its main idea is two-fold: 1) it designs a sensor-level federated learning framework, where each sensor uploads only gradient updates instead of raw data to optimize the global model, and 2) it proposes a local spatial sharing strategy, allowing sensors within the same spatial region to share their latent feature vectors, capturing spatial correlations and enhancing recovery accuracy. Experimental results on two real-world WSNs datasets demonstrate that the proposed model outperforms existing federated methods in terms of recovery performance.