  In this paper we consider the matching coefficient of the vector current
between Quantum Chromodynamics (QCD) and Non-Relativistic QCD (NRQCD) to
three-loop order in perturbation theory. We evaluate the fermionic corrections
containing a closed massless fermion loop. The results are building blocks both
for the bottom and top quark system at threshold. We explain in detail the
methods used for the evaluation of the Feynman diagrams, classify the occurring
master integrals and provide results for the latter. The numerical effects are
significant. They have the tendency to improve the behaviour of the
perturbative series -- both for the bottom and top quark system.
