A quantum-mechanical study has been carried out for a collinear rearrangement reaction He + H-2+ --> HeH+ + H both on a diatomics-in-molecules semi-empirical surface and on a fitted ab initio surface. The calculation for the fitted ab initio surface has been carried out with a fine mesh in a broad range of energies up to the dissociation threshold. The reaction probabilities for the H-2+ molecule initially in highly excited vibrational states are also reported.