Human activity recognition (HAR) using radio frequency (RF) signals has garnered considerable attention for its applications in smart environments. However, traditional systems often struggle with limited independent channels between transmitters and receivers, multipath fading, and environmental noise, which particularly degrades performance in through-the-wall scenarios. In this paper, we present a transmissive reconfigurable intelligent surface (TRIS)-assisted through-the-wall human activity recognition (TRIS-HAR) system. The system employs TRIS technology to actively reshape wireless signal propagation, creating multiple independent paths to enhance signal clarity and improve recognition accuracy in complex indoor settings. Additionally, we propose the Human intelligence Mamba (HiMamba), an advanced state space model that captures temporal and frequency-based information for precise activity recognition. HiMamba achieves state-of-the-art performance on two public datasets, demonstrating superior accuracy. Extensive experiments indicate that the TRIS-HAR system improves recognition performance from 85.00% to 98.06% in laboratory conditions and maintains high performance across various environments. This approach offers a robust solution for enhancing RF-based HAR, with promising applications in smart home and elderly care systems.