Modern Federated Learning (FL) has become increasingly essential for handling highly heterogeneous mobile devices. Current approaches adopt a partial model aggregation paradigm that leads to sub-optimal model accuracy and higher training overhead. In this paper, we challenge the prevailing notion of partial-model aggregation and propose a novel "full-weight aggregation" method named Moss, which aggregates all weights within heterogeneous models to preserve comprehensive knowledge. Evaluation across various applications demonstrates that Moss significantly accelerates training, reduces on-device training time and energy consumption, enhances accuracy, and minimizes network bandwidth utilization when compared to state-of-the-art baselines.