  A symmetry-preserving approach to the continuum bound-state problem in
quantum field theory is used to calculate the masses, leptonic decay constants
and light-front distribution amplitudes of empirically accessible heavy-light
mesons. The inverse moment of the $B$-meson distribution is particularly
important in treatments of exclusive $B$-decays using effective field theory
and the factorisation formalism; and its value is therefore computed:
$\lambda_B(\zeta = 2\,{\rm GeV}) = 0.54(3)\,$GeV. As an example and in
anticipation of precision measurements at new-generation $B$-factories, the
branching fraction for the rare $B\to \gamma(E_\gamma) \ell \nu_\ell$ radiative
decay is also calculated, retaining $1/m_B^2$ and $1/E_\gamma^2$ corrections to
the differential decay width, with the result $\Gamma_{B\to \gamma \ell
\nu_\ell}/\Gamma_B = 0.47(15)$ on $E_\gamma > 1.5\,$GeV.
