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: $λ_B(ζ= 2\,{\rm GeV}) = 0.54(3)\,$GeV. As an example and in anticipation of precision measurements at new-generation $B$-factories, the branching fraction for the rare $B\to γ(E_γ) \ell ν_\ell$ radiative decay is also calculated, retaining $1/m_B^2$ and $1/E_γ^2$ corrections to the differential decay width, with the result $Γ_{B\to γ\ell ν_\ell}/Γ_B = 0.47(15)$ on $E_γ> 1.5\,$GeV.

6 pages, 6 figure, 5 tables