  The decay $H\to \ell^+\ell^- \gamma$, $\ell=e,\mu$, receives contributions
from $H\to Z[\to \ell^+\ell^-] \gamma$ and a non-resonant contribution, both of
which are loop-induced. We describe how one can separate these sub-processes in
a gauge-independent way, define the decay rate $\Gamma(H\to Z\gamma)$, and
extract the latter from differential $H\to \ell^+\ell^- \gamma$ branching
ratios. For $\ell=\mu$ also the tree decay rate, which is driven by the muon
Yukawa coupling, is important. We propose kinematic cuts optimized to separate
the three contributions, paving the way to the milestones (i) discovery of
$H\to Z \gamma$, (ii) discovery of $H\to \mu^+\mu^- \left. \gamma\right|_{\rm
tree}$, and (iii) quantification of new physics in both the effective
$H$-$Z$-$\gamma$ and non-resonant $H$-$\ell^+$-$\ell^-$-$\gamma$ couplings.
