The aim of this work was to determine mass transfer coefficients for membrane-based extraction joined with membrane-based stripping (re-extraction). For the integrated system of batch extraction and back extraction (re-extraction) in a hollow fibre contactor, and for the extraction system exhibiting a high value of the distribution coefficient a model, which simplifies our previously derived model (parts I and II of this article), was proposed. This model consists of three relations resulting from analytical integration of the differential equations, which were used in the previous model. The model allows determining the overall mass transfer coefficients simultaneously for batch extraction and back extraction from the experimental time dependences of concentration of the transferred component in the reservoirs of the feed and stripping phases. The proposed model was applied for extraction of Zn from an aqueous phase to the solvent with DEHPA carrier and for simultaneous back extraction from the solvent to diluted sulfuric acid. For the extraction system with high distribution coefficient the resistance against mass transfer is concentrated predominantly in the aqueous phase. In this case, the particular coefficient, k(e), could be considered to be equal to the overall coefficient, K-e. The dependence of the measured values k(e) vs. Re in lumens was compared to k(e) values available in the literature. Moreover, a good agreement of the measured and calculated dependence of the concentration of the transferred component in the feed and stripping reservoirs confirmed the suitability of the presented model for the batch extraction/re-extraction circulating arrangement in case of membrane-based extraction joined with membrane-based stripping.