Achieving sub-percent precision in lattice QCD requires incorporating isospin-breaking (IB) effects from $m_u \neq m_d$ and QED. The RC* collaboration employs C-periodic boundary conditions (BCs) in spatial directions to implement QCD+QED on the lattice. This approach ensures that locality, gauge, and translational invariance are preserved throughout the calculations. In this talk, I will present our progress in computing the Hadronic Vacuum Polarization contribution to $(g-2)_\mu$ in QCD+QED. Specifically, we compare two methods for addressing IB effects: (1) fully dynamical QCD+QED simulations, and (2) the RM123 method applied to isospin-symmetric QCD; in both cases, utilizing C-periodic BCs. To facilitate the comparison, the analysis is performed at fixed lattice spacing and volume. I will conclude by outlining the other works in progress in our group.