Relation between the slope of the initial radial metallicity gradient in the satellite thin disc (f_sat, thin) and the slope of the metallicity gradient in the final distribution of all the thin disc stars in the E − L_z space as a function of energy (d⟨[Fe/H]⟩/dE), in the total volume of the simulation (solid lines), and in the restricted solar-like volume (dashed line). The case of ϕ_orb = 0° also features the dash-dotted curve described in Section 3.4.