Many mobile sensing applications utilize data from various modalities, including motion and physiological sensors in mobile and wearable devices. Federated Learning (FL) is particularly suitable for these applications thanks to its privacy-preserving feature. However, challenges such as limited battery life, poor network conditions, and sensor malfunctions can restrict the use of all available modalities for local model training. Additionally, existing multimodal FL systems also struggle with scalability and efficiency as the number of modality sources increases. To address these issues, we introduce FLISM, a framework designed to enable multimodal FL with incomplete modalities. FLISM leverages simulation technique to learn robust representations that can handle missing modalities and transfers model knowledge across clients with varying set of modalities. The evaluation results using three real-world datasets and simulations demonstrate FLISM's effective balance between model performance and system efficiency. It shows an average improvement of .067 in F1-score, while also reducing communication (2.69x faster) and computational (2.28x more efficient) overheads compared to existing methods addressing incomplete modalities. Moreover, in simulated scenarios involving tasks with a larger number of modalities, FLISM achieves a significant speedup of 3.23x~85.10x in communication and 3.73x~32.29x in computational efficiency.