Generalised model-independent characterisation of strong gravitational lenses II: Transformation matrix between multiple images

(shortened) We determine the transformation matrix T that maps multiple images with resolved features onto one another and that is based on a Taylor-expanded lensing potential close to a point on the critical curve within our model-independent lens characterisation approach. From T, the same information about the critical curve at fold and cusp points is derived as determined by the quadrupole moment of the individual images as observables. In addition, we read off the relative parities between the images, so that the parity of all images is determined, when one is known. We compare all retrievable ratios of potential derivatives to the actual ones and to those obtained by using the quadrupole moment as observable for two and three image configurations generated by a galaxy-cluster scale singular isothermal ellipse. We conclude that using the quadrupole moments as observables, the properties of the critical curve at the cusp points are retrieved to higher accuracy, at the fold points to lower accuracy, and the ratios of second order potential derivatives to comparable accuracy. We show that the approach using ratios of convergences and reduced shear is equivalent to ours close to the critical curve but yields more accurate results and is more robust because it does not require a special coordinate system like the approach using potential derivatives. T is determined by mapping manually assigned reference points in the images onto each other. If the assignment of reference points is subject to measurement uncertainties under noise, we find that the confidence intervals of the lens parameters can be as large as the values, when the uncertainties are larger than one pixel. Observed multiple images with resolved features are more extended than unresolved ones, so that higher order moments should be taken into account to improve the reconstruction.