The possible wave resonance in the narrow gap formed by the parallel arrangement of ships will lead to the sharp increase of wave loads and the rapid growth of motion response. The fluid resonance inside a narrow gap between two side-by-side boxes is investigated numerically based on an open-source CFD package, OpenFOAM. The upstream box remains fixed, while the downstream box is allowed to heave freely under wave actions. This work aims to examine the influence of the motion of the downstream box on the fluid resonant behaviors inside the gap. The hydrodynamic behaviors considered include the wave height inside the gap, the heave displacement, and the reflection, transmission, and energy loss coefficients. Gao et al. (2021) reported the influence of the motion of the upstream box on gap resonant behaviors. For comparative study, some results of Gao et al. (2021) are also presented in this work. It is found that the heave motion of any box in the two-box system leads to a smaller resonant wave height amplification and a larger fluid resonance frequency. The frequency at which the maximum heave displacement of the downstream box occurs is less than the fluid resonant frequency. The heave motion of any box in the two-box system results in a larger reflection coefficient and a smaller energy loss coefficient.