Based on deterministic and probabilistic forecast verification, we investigated the performance of three subseasonal-to-seasonal (S2S) operational models, i.e., the model of the European Centre for Medium-Range Weather Forecasts (ECMWF) and two models of the China Meteorological Administration (CMA1.0 and CMA2.0), in the extended-range forecast of extreme rainfall over southern China (SCER) while considering the modulation of 10-30-day boreal summer intraseasonal oscillation (BSISO2). The Heidke Skill Score (HSS) of the SCER in the ECMWF, CMA2.0, and CMA1.0 models decreased to less than 0.1 at lead times of 13, 9, and 6 days, respectively. Similarly, the useful prediction skill of the BSISO2 index in the ECMWF, CMA1.0, and CMA2.0 models was up to 15, 13, and 8 days in advance, respectively. The BSISO2's phase error, rather than the amplitude error, determines its prediction skill. The HSS of the BSISO2 index is significantly correlated with that of SCER in all three S2S models, suggesting that the prediction skill of SCER is influenced by that of BSISO2. The ECMWF shows much higher skill than the two CMA models do in predicting the SCER probability changes under the influence of BSISO2 during Phases 5-7, with the useful prediction skill having up to a 10-day lead time. In contrast, CMA1.0 and CMA2.0 can only predict the modulation of BSISO2 on the SCER probability within a week. The prediction skill of BSISO2's modulation on SCER largely relies on moisture convergence, rather than on moisture advection. This study highlighted the importance of model's accurate representation of BSISO2 and its associated moisture convergence for improving extended-range forecast of SCER.