Snapshots of the (L_z, L_⊥) distribution at 0, 2, 4, 6, and 8 Gyr of integration for 319 particles with Helmi-Stream-like phase-space positions, selected from the re-centred Progenitor 4 by Koppelman et al. (2019b), in a potential with a triaxial NFW halo with p = 1.02 and q = 1.18. The colourbar indicates the variation in L_z, calculated over an integration time of 100 Gyr. At t = 0 Gyr, the (L_z, L_⊥) distribution of the particles is positively correlated. The particles with ΔL_z ≳ 2000 are on y-tube orbits, meaning their L_z is no longer conserved, making them move towards lower L_z in time with respect to the particles on z-tube orbits, which have ΔL_z ≲ 1000. Particles with high initial L_⊥ are strongly trapped by the Ω_ϕ : Ω_z = 1:1 resonance (selected as ΔL_{y, z} ≲ 750), and are encircled in green. A video, showing the behaviour of the particles in (L_z, L_⊥) space over time, is available online.