For pt.I see ibid., vol.11, p.473-92 (1978). Test calculations to assess the accuracy achieved in various ways of using the method described in the first paper of this series, for laboratory energies around 25 keV amu-1 are reported. It is concluded that cross sections for electron capture into the n=2 states, earlier published by the authors for H+-H collisions at 25 keV, should be fairly accurate, while the errors in the excitation cross sections may be larger. For He2+-H collisions, cross sections for capture into the n=1 and n=2 states at incident energies of 19.4, 41.7 and 50 keV amu-1 are presented. On the basis of our test calculations, it is hoped that the cross sections for capture into the n=2 states are accurate to about 10%.