A search is reported for long-lived dark photons with masses between 0.1 GeV and 15 GeV, from exotic decays of Higgs bosons produced via vector-boson-fusion. Events that contain displaced collimated Standard Model fermions reconstructed in the calorimeter or muon spectrometer are probed. This search uses the full LHC Run 2 (2015–2018) data sample collected in proton–proton collisions at $\sqrt{s}=13$ TeV, corresponding to an integrated luminosity of 139 $fb^{-1}$. Dominant backgrounds from Standard Model processes and non-collision sources are estimated using data-driven techniques. The observed event yields in the signal regions are consistent with the expected background. Upper limits on the Higgs boson to dark photon branching fraction are reported as a function of the dark photon mean proper decay length or of the dark photon mass and the coupling between the Standard Model and the potential dark sector. This search is combined with previous ATLAS searches obtained in the gluon–gluon fusion and WH production modes. A branching fraction above 10% is excluded at 95% CL for a 125 GeV Higgs boson decaying into two dark photons for dark photon mean proper decay lengths between 173 and 1296 mm and mass of 10 GeV.