Hippocampal sharp-wave ripples (SWRs) are transient high-frequency oscillations essential for memory recall and consolidation during non-rapid eye movement (NREM) sleep. While synchronous replay of firing sequences in the hippocampus and neocortex during slow-wave sleep (SWS) has been observed, the mechanisms governing ripple propagation in cortical networks remain underexplored. Temporal coupling between sleep rhythms, such as slow oscillations (SOs), spindles, and ripples, is critical for memory consolidation, but the specific role of SO-ripple coupling in facilitating inter-areal communication is unclear. In this study, we used a computational hippocampal-cortical network model to investigate how ripples are transmitted to cortical areas. We found that inter-areal connection probability and strength co-modulate ripple transmission, with denser and stronger connections promoting communication. SOs facilitated ripple transmission under weaker connections when ripples preceded SO peaks, reflecting an energy-efficiency trade-off in brain coordination during memory consolidation.