In this contribution we present a lattice calculation of the leading-order electromagnetic and strong isospin-breaking (IB) corrections to the quark-connected hadronic-vacuum-polarization (HVP) contribution to the anomalous magnetic moment of the muon. The results are obtained adopting the RM123 approach in the quenched-QED approximation and using the QCD gauge configurations generated by the ETM Collaboration with N f = 2 + 1 + 1 dynamical quarks, at three values of the lattice spacing (a 0.062, 0.082, 0.089 fm), at several lattice volumes and with pion masses between 210 and 450 MeV. After the extrapolations to the physical pion mass and to the continuum and infinite-volume limits the contributions of the light, strange and charm quarks are respectively equal to δ a HVP µ (ud) = 7.1 (2.5) · 10 −10 , δ a HVP µ (s) = −0.0053 (33) · 10 −10 and δ a HVP µ (c) = 0.0182 (36) · 10 −10 . At leading order in α em and (m d − m u )/Λ QCD we obtain δ a HVP µ (udsc) = 7.1 (2.9) · 10 −10 , which is currently the most accurate determination of the IB corrections to a HVP µ .