Satellite free-space optical (FSO) communication is very promising in improving the bandwidth and capacity of space information networks in the future. However, the inter-satellite transmission distance of over 1000 km leads to unstable optical beam pointing, acquisition, and tracking and then generates optical power jitter by a large margin before detection-demodulation. Therefore, it is difficult to realize high-stability and long-time FSO communication between satellites due to the generated bit error rate (BER) by jitter. In this paper, we report an autonomously self-designed and high-integration laser communication payload (LCP) and on-orbit-demonstrated inter-satellite 145 min, zero-BER FSO stable communication with a line rate of 2.8 Gbps. Moreover, based on the inter-satellite laser communication link, a video phone was clearly implemented for more than 10 min, and authentic user data transmitted 459,149 packets, achieving results of zero-packet loss. Summarily, this on-orbit experiment demonstrated an excellent performance of the LCP owing to the distinctive design of integrating a high-power amplifier and low-noise amplifier optical amplification function. Our space mission was successfully completed, and the on-orbit demonstration results may offer a significant reference for the field of satellite laser communication and space information networks.