Galaxies undergo numerous transformative processes throughout their lifetimes that ultimately lead to the expulsion of gas and the cessation of star-forming activity. This phenomenon is commonly known as quenching, and in this study, we delve into the possibility that this process is caused by the environmental processes associated with the surrounding cluster. To this end, we used the results of our previous paper - where we analyzed dwarf galaxies in the SAMI-Fornax survey together with massive galaxies from the ATLAS(3D) survey - to compute the quenching time of each galaxy and compare it with the infall time into the cluster. Using t(90) as an approximation of the quenching time and deriving the infall time from phase-space models, we determined the probability of the quenching being produced by the local environment of galaxies. Our results reveal a relation between galaxy mass and quenching probability. Massive galaxies, down to M-star similar to 10(10)M(circle dot), exhibit a low, almost zero probability of quenching, suggesting their independence of environmental effects. As we move into the mass regime of dwarf galaxies, the probability increases with decreasing mass, highlighting their sensitivity to environmental quenching. For dwarfs, 36 +/- 9% of our observational data are consistent with this hypothesis, challenging the idea that the present-day cluster, Fornax, is the primary driver of quenching in the low-mass galaxies of our sample with stellar mass from 10(7) to 10(9)M(circle dot). To further investigate the importance of environmental processes, we compared these results with cosmological simulations, selecting galaxies under similar conditions to our observational sample. Remarkably, the simulated sample shows lower quenching probabilities as we move down in mass, and barely 5 +/- 1% of galaxies meet the quenching criteria. This discrepancy between observations and simulations underlines the fact that the modelling of quenching is still in its infancy. In general, the number of observed galaxies quenched by their environment is lower than expected, which suggests that preprocessing plays a larger role in galaxy evolution. Ultimately, our results highlight the need for higher-quality simulations and refinement of galaxy formation and evolution models.