Federated Class-Incremental Learning (FCIL) focuses on continually transferring the previous knowledge to learn new classes in dynamic Federated Learning (FL). However, existing methods do not consider the trustworthiness of FCIL, i.e., improving continual utility, privacy, and efficiency simultaneously, which is greatly influenced by catastrophic forgetting and data heterogeneity among clients. To address this issue, we propose FedProK (Federated Prototypical Feature Knowledge Transfer), leveraging prototypical feature as a novel representation of knowledge to perform spatial-temporal knowledge transfer. Specifically, FedProK consists of two components: (1) feature translation procedure on the client side by temporal knowledge transfer from the learned classes and (2) prototypical knowledge fusion on the server side by spatial knowledge transfer among clients. Extensive experiments conducted in both synchronous and asynchronous settings demonstrate that our FedProK outperforms the other state-of-the-art methods in three perspectives of trustworthiness, validating its effectiveness in selectively transferring spatial-temporal knowledge.