  We present results for the charged kaon-box contributions to the hadronic
light-by-light (HLBL) correction of the muon's anomalous magnetic moment. To
this end we determine the kaon electromagnetic form factor within the
functional approach to QCD using Dyson-Schwinger and Bethe-Salpeter equations
and evaluate the kaon-box contribution as defined in the dispersive approach to
HLBL. As an update to previous work we also re-evaluate the charged pion-box
contribution taking effects due to isospin breaking into account. Our results
are $a_\mu^{\pi^\pm-\text{box}} = -15.7 \,(2)(3) \times 10^{-11}$ and
$a_\mu^{K^\pm-\text{box}} = -0.48 \,(2)(4) \times 10^{-11}$ thus confirming the
large suppression of box contributions beyond the leading pion box.
