Cross sections for electron capture by (^4)He(^2+) ions from ground state atomic hydrogen are presented for a (^4)He(^2+) laboratory energy range from 1 to 800 keV (0.25 to 200 keV amu (^-1)). The cross sections were calculated using a coupled channel approximation in which the electronic wavefunction was expanded in terms of a finite number of atomic orbital basis states centred upon the target and the projectile. Electron translation factors which incorporated a switching function were included in the basis states. The semi-classical impact parameter approximation was employed. The cross sections presented are for electron capture into the 2s state of (^4)Me(^+), and into the n = 2 level of (^4)He(^+) using two states and four states respectively in the basis expansion. Four functional forms of switching function were used in the translation factors. The cross sections are compared with ones calculated using two-state and four-state atomic basis expansions which used plane-wave translation factors, and also with other theoretical and experimental cross sections. For energies ≤ 2.5 keV amu (^-1) fairly reasonable agreement is obtained with other data. For energies ≥ 2.5 keV amu (^-1) the present cross sections are in poor to extremely poor agreement with other data, steady divergence of the present results from existing data being observed with increasing energy. The present results are discussed, and conclusions and suggestions for future work are made.