The Atlantic Meridional Overturning Circulation (AMOC) and polar ice sheets are coupled tipping elements, allowing for potential cascading tipping events in which tipping is facilitated by their mutual interactions. However, while an AMOC destabilization driven by Greenland Ice Sheet (GIS) meltwater release is well documented, the consequences of a West Antarctic Ice Sheet (WAIS) tipping on the AMOC remain unclear. In the Earth System Model of Intermediate Complexity CLIMBER-X, we perform experiments where meltwater fluxes representing plausible tipping trajectories of the GIS and WAIS are applied. We find that WAIS meltwater input can increase the AMOC resilience to GIS meltwater. In particular, we show that this stabilizing effect can cause the AMOC recovery and, for the first time in a comprehensive model, totally prevent an AMOC collapse. Moreover, we find this stabilzation to occur for ice sheet tipping trajectories that are relevant under high future greenhouse gas emission scenarios.