There have been efforts to simplify analysis of a complex system by relating it to a simpler system through certain system relations. In this paper, we consider continuous-time systems related by a graph simulation relation and focus on preservation of input-output-to-state stability (IOSS) and its integral variant, integral IOSS (iTOSS). We establish that, under mild continuity and boundedness assumptions on some appropriately defined set-valued functions, the (i)IOSS property for the simulating system can lead to the (i)IOSS property for the original simulated system. The results thus demonstrate the possibility of inferring the (i)IOSS of a system by analyzing a potentially simpler system.