Federated Learning, a new machine learning paradigm enhancing the use of edge devices, is receiving a lot of attention in the pervasive community to support the development of smart services. Nevertheless, this approach still needs to be adapted to the specificity of the pervasive domain. In particular, issues related to continual learning need to be addressed. In this paper, we present a distillation-based approach dealing with catastrophic forgetting in federated learning scenario. Specifically, Human Activity Recognition tasks are used as a demonstration domain.