This paper is part of an effort to correct the transmission spectra of a transiting planet orbiting an active star. In Paper I (Cracchiolo, Micela & Peres 2020), we have demonstrated a methodology to minimize the potential bias induced by unocculted star spots on the transmission spectrum, assuming a spot model parametrized by filling factor and temperature. In this work, we introduce the limb-darkening effect, therefore the position of the spot in the stellar disc and the impact parameter of the transiting planet now play a key role. The method is tested on simulations of planetary transits of three representative kinds of planetary systems, at ARIEL resolution. We find that a realistic treatment of the limb darkening is required to reliably estimate both the spots parameters and the transmission spectrum of the transiting planet. Furthermore, we show that the influence of the spots on the retrieval of the planetary transmission spectrum is significant for spots close to the centre of the star, covering a fraction greater than 0.05 and with a temperature contrast greater than $500\, {\rm K}$, and that for these cases our method can confidently extract the transmission spectrum and the impact parameter of the transiting planet for both cases of occulted and not occulted spots, provided that we have an accurate characterization of the stellar parameters and a reliable simulator of the instrument performances.