  We evaluate the corrections to the matching coefficient of the vector current
between Quantum Chromodynamics (QCD) and Non-Relativistic QCD (NRQCD) to
three-loop order containing a closed heavy-fermion loop. The result constitutes
a building block both for the bottom- and top-quark system at threshold. Strong
emphasis is put on our completely automated approach of the calculation
including the generation of the Feynman diagrams, the identification of the
topologies, the reduction to master integrals and the automated numerical
computation of the latter.
