  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 by 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 \textit{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.
