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Due to the widespread dissemination of rumors on social media platforms, detecting rumors has been a long-standing concern for various communities. However, existing rumor detection methods rarely consider the fairness issues inherent in the model, which can lead to biased predictions across different stakeholder groups (e.g., domains and originating platforms of the detected content), also undermining their detection effectiveness. In this work, we propose a two-step framework to address this issue. First, we perform unsupervised partitioning to dynamically identify potential unfair data patterns without requiring sensitive attribute annotations. Then, we apply invariant learning to these partitions to extract fair and informative feature representations that enhance rumor detection. Extensive experiments show that our method outperforms strong baselines regarding detection and fairness performance, and also demonstrate robust performance on out-of-distribution samples. Further empirical results indicate that our learned features remain informative and fair across stakeholder groups and can correct errors when applied to existing baselines.