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 ($a \simeq 0.062, 0082, 0.089$ fm) with pion masses in the range $M_\pi \simeq 210 - 450$ MeV. Neglecting disconnected diagrams and after the extrapolations to the physical pion mass and to the continuum limit we obtain: $a_\mu^s(\alpha_{em}^2) = (53.1 \pm 2.5) \cdot 10^{-10}$, $a_\mu^s(\alpha_{em}^3) = (-0.091 \pm 0.021) \cdot 10^{-10}$, $a_\mu^c(\alpha_{em}^2) = (14.75 \pm 0.56) \cdot 10^{-10}$ and $a_\mu^c(\alpha_{em}^3) = (-0.202 \pm 0.023) \cdot 10^{-10}$ for the strange and charm quark contributions, respectively. Preliminary results for the light quark contribution will be presented.