As an emerging distributed paradigm, Federated Learning (FL) facilitates collaborative training among multiple clients without sharing the raw data. However, the classic FL still faces significant challenges due to feature/model heterogeneity and catastrophic forgetting, which seriously hamper effective knowledge transfer and cause the forgetting of previously acquired knowledge. To address these challenges, we propose FBCL, a novel generalizable heterogeneity-aware Federated features and Basic-matrix Consistency Learning to balance intra-domain discriminability and inter-domain generalization. For the heterogeneity issue, we align the similarity of feature distribution and construct the high-dimensional basic matrix by using irrelevant unlabeled data, thereby overcoming communication barriers and learning generalizable representations while maintaining strict privacy preservation. For the catastrophic forgetting issue during local updating, we introduce constraints in high-dimensional features to retain inter-domain knowledge, and then extract accurate knowledge by distilling old models to preserve worthy historical information. Using real-world unlabeled public datasets, extensive experiments validate the superiority of the proposed FBCL, which outperforms state-of-the-art methods on various scenarios of image classification.