The integration of space and terrestrial networks results in a promising future network architecture, which exploits the high data rate and low latency of terrestrial networks as well as the wide-range coverage of satellite networks. However, spaceground integrated networks (SGINs) face some unprecedented challenges, including the rapidly fluctuating network topology, limited resources, intermittent connections, lossy links, asymmetric bandwidth allocation, and so on. The traditional endto- end (E2E) transport protocols designed for reliable terrestrial networks exhibit inherent limitations in the context of dynamic SGIN. A promising solution is to decouple the E2E perfect reception confirmation into hop-by-hop acknowledgments, which results in prompt packet loss recovery and high transmission resilience in the face of high-dynamic topologies. Hence, in this paper we propose a reliable cache-enabled transport system, which enhances the efficiency of reliable hop-by-hop transmission, and supports multi-orbit breakpoint transmission, while at the same time facilitates the reliability of intra-satellite communication with a novel transport protocol. In addition to unveiling a compelling system-level design, we demonstrate the benefits of the proposed reliable transport system (RTS) in a real SGIN prototype relying on satellites having onboard processing capability. Our experimental results validate the feasibility of the proposed RTS in the face of lossy links, intermittent connections and intra-satellite transmission failure. Moreover, one of the satellites has been launched in April 2021, while the other two will be launched to perform on-orbit test.