Distribution in E – L_z of a set of ten clusters accreted together with their progenitor galaxy on a MW-type galaxy through one of the N-body simulations presented in Pagnini et al. (2023) (identified in that paper with the ID=MWsat_nl_Φ180). Clusters are colour-coded according to their escape time from the progenitor satellite, which is defined as the time when the distance between the GC and the satellite’s centre of mass is larger than 15 kpc (see Sect. 3 in Pagnini et al. 2023 for the details). In the background, the distribution of field stars of the accreted satellite is also shown as a density map. Energies and angular momenta have been re-scaled to obtain a distribution comparable with that of the Galactic GCs and field stars presented in Fig. 7.