  Recently, both ATLAS and CMS measured the decay $h\to\mu^+\mu^-$, finding a
signal strength with respect to the Standard Model expectation of $1.2\pm0.6$
and $1.19\substack{+0.41+0.17\\-0.39 -0.16}$, respectively. This provides, for
the first time, evidence that the Standard Model Higgs couples to second
generation fermions. This measurement is particularly interesting in the
context of the intriguing hints for lepton flavor universality violation,
accumulated within recent years, as new physics explanations could also be
tested in the $h\to\mu^{+}\mu^{-}$ decay mode. Leptoquarks are prime candidates
to account for the flavor anomalies. In particular, they can provide the
necessary chiral enhancement (by a factor $m_t/m_\mu$) to address $a_\mu$ with
TeV scale new physics. In this letter we point out that such explanations of
$a_\mu$ also lead to enhanced effects in $h\to\mu^+\mu^-$ and we examine the
correlations between $h\to\mu^+\mu^-$ and $a_\mu$ within leptoquark models. We
find that the effect in the branching ratio of $h\to\mu^+\mu^-$ ranges from
several percent up to a factor three, if one aims at accounting for $a_\mu$ at
the $2\,\sigma$ level. Hence, the new ATLAS and CMS measurements already
provide important constraints on the parameter space, rule out specific $a_\mu$
explanations and will be very important to test the flavor anomalies in the
future.
