Solution
= Solution
True. Slide beads upward separately in each of the refined residue classes modulo $ef$. Grouping the refined runners first by residue modulo $f$ and then packing each component modulo $e$ produces $C_e(Q_f(\lambda))$. Packing modulo $ef$ before forgetting the refinement produces $Q_f(C_{ef}(\lambda))$. These are the same runner configurations, so
$$
C_e(Q_f(\lambda))=Q_f(C_{ef}(\lambda)).
$$