We derive an expression for the charge-exchange cross section σ(N) for the formation of excited final states with principal quantum number N in the limit N > 1. This provides a rigorous proof of the results made plausible by Butler and Johnston in the preceding paper.We also derive a closed expression for the fractional contribution to σ(N) made by the various angular momentum states (l = 0, 1, 2, ... , N − 1). For high energies only S states contribute: in the neighbourhood of the resonance in σ(N) both P and D states are also formed in significant amounts. (At the resonance σ(N) comprises 29% S states, 54% P states and 15% D states.)