In this paper, we propose a new task of cross-modal federated human activity recognition (CMF-HAR), which is conducive to promote the large-scale use of the HAR model on more local devices. To address the new task, we propose a feature-disentangled activity recognition network (FDARN), which has five important modules of altruistic encoder, egocentric encoder, shared activity classifier, private activity classifier and modality discriminator. The altruistic encoder aims to collaboratively embed local instances on different clients into a modality-agnostic feature subspace. The egocentric encoder aims to produce modality-specific features that cannot be shared across clients with different modalities. The modality discriminator is used to adversarially guide the parameter learning of the altruistic and egocentric encoders. Through decentralized optimization with a spherical modality discriminative loss, our model can not only generalize well across different clients by leveraging the modality-agnostic features but also capture the modality-specific discriminative characteristics of each client. Extensive experiment results on four datasets demonstrate the effectiveness of our method.