The increasing emphasis on privacy in recommendation systems has led to the adoption of Federated Learning (FL) as a privacy-preserving solution, enabling collaborative training without sharing user data. While Federated Recommendation (FedRec) effectively protects privacy, existing methods struggle with non-stationary data streams, failing to maintain consistent recommendation quality over time. On the other hand, Continual Learning Recommendation (CLRec) methods address evolving user preferences but typically assume centralized data access, making them incompatible with FL constraints. To bridge this gap, we introduce Federated Continual Recommendation (FCRec), a novel task that integrates FedRec and CLRec, requiring models to learn from streaming data while preserving privacy. As a solution, we propose F3CRec, a framework designed to balance knowledge retention and adaptation under the strict constraints of FCRec. F3CRec introduces two key components: Adaptive Replay Memory on the client side, which selectively retains past preferences based on user-specific shifts, and Item-wise Temporal Mean on the server side, which integrates new knowledge while preserving prior information. Extensive experiments demonstrate that F3CRec outperforms existing approaches in maintaining recommendation quality over time in a federated environment.