  The $B$-meson decay constant can be measured on the lattice using a $1/m_b$
expansion. To relate the physical quantity to Monte Carlo data one has to know
the renormalization coefficient, $Z$, between the lattice operators and their
continuum counterparts. We come back to this computation to resolve
discrepancies found in previous calculations. We define and discuss in detail
the renormalization procedure that allows the (perturbative) computation of
$Z$. Comparing the one-loop calculations in the effective Lagrangian approach
with the direct two-loop calculation of the two-point $B$-meson correlator in
the limit of large $b$-quark mass, we prove that the two schemes give
consistent results to order $\alpha_s$. We show that there is, however, a
renormalization prescription ambiguity that can have sizeable numerical
consequences. This ambiguity can be resolved in the framework of an $O(a)$
improved calculation, and we describe the correct prescription in that case.
Finally we give the numerical values of $Z$ that correspond to the different
types of lattice approximations discussed in the paper.
