The probability amplitude for proton-hydrogen ground-state electron capture at 125 keV in the boundary-corrected second Born approximation has been evaluated numerically by retaining all significant bound and continuum hydrogenic intermediate states for which the orbital angular momentum l<or=3. The differential cross section is found to be in good agreement with the experimental data for scattering angles less than about 1 mrad in the centre of mass system. The value of the boundary-corrected second Born total cross section is similar to that obtained in the boundary-corrected first Born approximation.