  We have explored how the electrical ($\sigma_{\rm el}$) and thermal
($\kappa$) conductivities in a thermal QCD medium get affected in weak-momentum
anisotropies arising either due to a strong magnetic field or due to asymptotic
expansion. This study facilitates to understand the longevity of strong
magnetic field through $\sigma_{el}$, Lorenz number in Wiedemann-Franz law, and
the validity of equilibrium by the Knudsen number. We calculate the
conductivities by solving relativistic Boltzmann transport equation in
relaxation-time approximation within quasiparticle model at finite T and strong
B. We have found that $\sigma_{el}$ and $\kappa$ get enhanced in a magnetic
field-driven anisotropy, but $\sigma_{el}$ decreases with temperature, opposite
to its faster increase in expansion-driven anisotropy. Whereas $\kappa$
increases slowly with temperature, contrary to its rapid increase in
expansion-driven anisotropy. The above findings are broadly attributed to three
factors: the stretching and squeezing of distribution function in anisotropies
generated by the magnetic field and asymptotic expansion, respectively, the
dispersion relation and resulting phase-space factor, the relaxation-time in
absence and presence of strong magnetic field. So $\sigma_{\rm el}$ extracts
the time-dependence of magnetic field, which decays slower than in vacuum but
expansion-driven anisotropy makes the decay faster. The variation in $\kappa$
transpires that Knudsen number decreases with T but expansion-driven anisotropy
reduces its value and magnetic field-driven anisotropy raises its value but to
less than one, thus the system can still be in equilibrium. The ratio,
$\kappa/\sigma_{el}$ in magnetic field-driven anisotropy increases linearly
with temperature but with a value smaller than in expansion-driven anisotropy.
Thus the Lorenz number can make the distinction between different anisotropies.
