Strong lensing has been employed extensively to obtain accurate mass measurements within the Einstein radius. We here use strong lensing to probe mass distributions beyond the Einstein radius. We consider SL2S J08544-0121, a galaxy group at redshift z=0.35 with a bimodal light distribution and with a strong lensing system located at one of the two luminosity peaks separated by ~54". The main arc and the counter-image of the strong lensing system are located at ~5" and ~8" from the lens galaxy centre. We find that a simple elliptical isothermal potential cannot satisfactorily reproduce the strong lensing observations. However, with a mass model for the group built from its light-distribution with a smoothing factor s and a mass-to-light ratio M/L, we obtain an accurate reproduction of the observations. We find M/L = 98 ± 27 (i band, solar units, not corrected for evolution) and s = 20" ± 9 (2σ confidence level). Moreover, we use weak lensing to independently estimate the mass of the group, and find a consistent M/L in the range 66-146 (1-σ confidence level). This suggests that light is a good tracer of mass. Interestingly, this also shows that a strong lensing-only analysis (on scales of ~10") can constrain the properties of nearby objects (on scales of ~100"). We characterise the type of perturbed strong lensing system that allows such an analysis: a non dominant strong lensing system used as a test particle to probe the main potential. This kind of analysis needs to be validated with other systems because it could provide a quick way of probing the mass distribution of clusters and groups. This is particularly relevant in the context of forthcoming wide-field surveys, which will yield thousands of strong lenses, some of which perturbed enough to pursue the analysis proposed in this paper.