The rise of End-Edge-Cloud Collaboration (EECC) offers a promising paradigm for Artificial Intelligence (AI) model training across end devices, edge servers, and cloud data centers, providing enhanced reliability and reduced latency. Hierarchical Federated Learning (HFL) can benefit from this paradigm by enabling multi-tier model aggregation across distributed computing nodes. However, the potential of HFL is significantly constrained by the inherent heterogeneity and dynamic characteristics of EECC environments. Specifically, the uniform model structure bounded by the least powerful end device across all computing nodes imposes a performance bottleneck. Meanwhile, coupled heterogeneity in data distributions and resource capabilities across tiers disrupts hierarchical knowledge transfer, leading to biased updates and degraded performance. Furthermore, the mobility and fluctuating connectivity of computing nodes in EECC environments introduce complexities in dynamic node migration, further compromising the robustness of the training process. To address multiple challenges within a unified framework, we propose End-Edge-Cloud Federated Learning with Self-Rectified Knowledge Agglomeration (FedEEC), which is a novel EECC-empowered FL framework that allows the trained models from end, edge, to cloud to grow larger in size and stronger in generalization ability. FedEEC introduces two key innovations: (1) Bridge Sample Based Online Distillation Protocol (BSBODP), which enables knowledge transfer between neighboring nodes through generated bridge samples, and (2) Self-Knowledge Rectification (SKR), which refines the transferred knowledge to prevent suboptimal cloud model optimization. The proposed framework effectively handles both cross-tier resource heterogeneity and effective knowledge transfer between neighboring nodes, while satisfying the migration-resilient requirements of EECC.