Federated Learning (FL) is to allow multiple clients to collaboratively train a model while keeping their data locally. However, existing FL approaches typically assume that the data in each client is static and fixed, which cannot account for incremental data with domain shift, leading to catastrophic forgetting on previous domains, particularly when clients are common edge devices that may lack enough storage to retain full samples of each domain. To tackle this challenge, we propose Federated Domain-Incremental Learning via Synergistic Replay (SR-FDIL), which alleviates catastrophic forgetting by coordinating all clients to cache samples and replay them. More specifically, when new data arrives, each client selects the cached samples based not only on their importance in the local dataset but also on their correlation with the global dataset. Moreover, to achieve a balance between learning new data and memorizing old data, we propose a novel client selection mechanism by jointly considering the importance of both old and new data. We conducted extensive experiments on several datasets of which the results demonstrate that SR-FDIL outperforms state-of-the-art methods by up to 4.05% in terms of average accuracy of all domains.