  We re-examine the possibility to measure the photon polarization in $B \to
K^*\gamma$ decays, via decays in which the photon subsequently undergoes
nuclear conversion to a lepton pair. We obtain compact expressions for the full
decay-plus-conversion amplitude. With these results we show that interference
between the $B \to (K^*\to K\pi)\gamma$ decay and the $\gamma N \to
\ell^+\ell^-N$ conversion permits both the ratio and relative weak phase
between the left- and right-handed photon amplitudes to be probed by an angular
observable, constructed from the final state dilepton, kaon and pion kinematic
configuration. Exploiting this technique will be experimentally challenging.
However, we present special kinematic cuts that enhance the statistical power
of this technique by an $\mathcal{O}(1)$ factor. We verify this effect and
extract pertinent angular kinematic distributions with dedicated numerical
simulations.
