In this work we use strong gravitational lensing techniques to constrain the total mass distribution of the galaxy cluster RXC J2248.7-4432 (RXC J2248, zlens = 0.348), also known as Abell S1063, observed within the Cluster Lensing And Supernova survey with Hubble (CLASH). Thanks to its strong lensing efficiency and exceptional data quality from the VIsible Multi-Object Spectrograph (VIMOS) and Multi Unit Spectroscopic Explorer (MUSE) on the Very Large Telescope, we can build a parametric model for the total mass distribution. Using the positions of the multiple images generated by 7 multiply-lensed background sources with measured spectroscopic redshifs, we find that the best-fit parametrisation for the cluster total mass distribution is composed of an elliptical pseudo-isothermal mass distribution with a significant core for the overall cluster halo, and of truncated pseudo-isothermal mass profiles for the cluster galaxies. This model is capable to predict the positions of the multiple images with an unprecedented precision of ≈ 0".3. We also show that varying freely the cosmological parameters of the ΛCDM model, our strong lensing model can constrain the underlying geometry of the universe via the angular diameter distances between the lens and the sources and the observer and the sources.