The Antarctic ozone hole has led to substantial changes in the Southern Hemisphere atmospheric circulation, such as the strengthening and poleward shift of the midlatitude westerly jet. Ozone recovery during the twenty-first century is expected to continue to affect the jet's strength and position, leading to changes in the opposite direction compared to the twentieth century and competing with the effect of increasing greenhouse gases. Simulations of the Earth's past and future climate, such as those performed for the Coupled Model Intercomparison Project Phase 6 (CMIP6), require an accurate representation of these ozone effects. Climate models that use prescribed ozone fields lack the important feedbacks between ozone chemistry, radiative heating, dynamics, and transport. In addition, when the prescribed ozone field was not generated by the same model to which it is prescribed, the imposed ozone hole is inconsistent with the simulated dynamics. These limitations ultimately affect the climate response to ozone depletion. This study investigates the impact of prescribing the ozone field recommended for CMIP6 on the simulated effects of ozone depletion in the Southern Hemisphere. We employ a new state-of-the-art coupled climate model, Flexible Ocean Climate Infrastructure (FOCI), to compare simulations in which the CMIP6 ozone is prescribed with simulations in which the ozone chemistry is calculated interactively. At the same time, we compare the roles played by ozone depletion and by increasing concentrations of greenhouse gases in driving changes in the Southern Hemisphere atmospheric circulation using a series of historical sensitivity simulations. FOCI captures the known effects of ozone depletion, simulating an austral spring and summer intensification of the midlatitude westerly winds and of the Brewer-Dobson circulation in the Southern Hemisphere. Ozone depletion is the primary driver of these historical circulation changes in FOCI. The austral spring cooling of the polar cap in the lower stratosphere in response to ozone depletion is weaker in the simulations that prescribe the CMIP6 ozone field. We attribute this weaker response to a prescribed ozone hole that is different to the model dynamics and is not collocated with the simulated polar vortex, altering the strength and position of the planetary wavenumber one. As a result, the dynamical contribution to the ozone-induced austral spring lower-stratospheric cooling is suppressed, leading to a weaker cooling trend. Consequently, the intensification of the polar night jet is also weaker in the simulations with prescribed CMIP6 ozone. In contrast, the differences in the tropospheric westerly jet response to ozone depletion fall within the internal variability present in the model. The persistence of the Southern Annular Mode is shorter in the prescribed ozone chemistry simulations. The results obtained with the FOCI model suggest that climate models that prescribe the CMIP6 ozone field still simulate a weaker Southern Hemisphere stratospheric response to ozone depletion compared to models that calculate the ozone chemistry interactively.