This paper shows the extensions of the authors' previous work on absolute cross sections for electron capture into He+ (4l) states, produced in collisions of He2+ with atomic and molecular hydrogen, to higher impact energies (27-132 keV amu-1) than used before (2-13 keV amu-1). The cross sections have been deduced from photon emission profile measurements along the ion beam axis, detecting the He II(n=4 to n=3) radiation at a wavelength of 4686 AA. The results for collisions with atomic hydrogen generally show reasonable agreement with the atomic orbital calculations of Fritsch (1989) below 50 keV amu-1 and at the highest impact energies used (E>or=100 keV amu-1) approach the data of the distorted wave approximation by Belkic et al. (1990).