Continuous behavioural authentication methods add a unique layer of security by allowing individuals to verify their unique identity when accessing a device. Maintaining session authenticity is now feasible by monitoring users' behaviour while interacting with a mobile or Internet of Things (IoT) device, making credential theft and session hijacking ineffective. Such a technique is made possible by integrating the power of artificial intelligence and Machine Learning (ML). Most of the literature focuses on training machine learning for the user by transmitting their data to an external server, subject to private user data exposure to threats. In this paper, we propose a novel Federated Learning (FL) approach that protects the anonymity of user data and maintains the security of his data. We present a warmup approach that provides a significant accuracy increase. In addition, we leverage the transfer learning technique based on feature extraction to boost the models' performance. Our extensive experiments based on four datasets: MNIST, FEMNIST, CIFAR-10 and UMDAA-02-FD, show a significant increase in user authentication accuracy while maintaining user privacy and data security.