  We present a lattice calculation of the Hadronic Vacuum Polarization (HVP)
contribution of the strange and charm quarks to the anomalous magnetic moment
of the muon including leading-order electromagnetic corrections. We employ the
gauge configurations generated by the European Twisted Mass Collaboration
(ETMC) with $N_f = 2+1+1$ dynamical quarks at three values of the lattice
spacing ($a \simeq 0.062, 0.082, 0.089$ fm) with pion masses in the range
$M_\pi \simeq 210 - 450$ MeV. The strange and charm quark masses are tuned at
their physical values. Neglecting disconnected diagrams and after the
extrapolations to the physical pion mass and to the continuum limit we obtain:
$a_\mu^s(\alpha_{em}^2) = (53.1 \pm 2.5) \cdot 10^{-10}$,
$a_\mu^s(\alpha_{em}^3) = (-0.018 \pm 0.011) \cdot 10^{-10}$ and
$a_\mu^c(\alpha_{em}^2) = (14.75 \pm 0.56) \cdot 10^{-10}$,
$a_\mu^c(\alpha_{em}^3) = (-0.030 \pm 0.013) \cdot 10^{-10}$ for the strange
and charm contributions, respectively.
