  Direct muon transfer in low-energy collisions of the muonic hydrogen H$_\mu$
and helium (He$^{++}$) is considered in a three-body quantum-mechanical
framework of coordinate-space integro-differential Faddeev-Hahn-type equations
within two- and six-state close coupling approximations. The final-state
Coulomb interaction is treated without any approximation employing appropriate
Coulomb waves in the final state. The present results agree reasonably well
with previous semiclassical calculations.
