We analyse the phenomenological implications of a light Higgs boson, $h$, within the CP-conserving 2-Higgs Doublet Model (2HDM) Type-I, for the detection prospects of the charged $H^pm$ state at Run II of the Large Hadron Collider (LHC), assuming $sqrt{s}=13$ TeV as energy and ${cal O}(100~{rm fb}^{-1})$ as luminosity. When sufficiently light, this $h$ state can open up the bosonic decay channel $H^pm to W^{pm(*)}h$, which may have a branching ratio significantly exceeding those of the $H^pm to tau u$ and $H^pm to cs$ channels. We perform a broad scan of the 2HDM Type-I parameter space, assuming the heavier of the two CP-even Higgs bosons, $H$, to be the observed SM-like state with a mass near 125 GeV. Through these scans we highlight regions in which $m_{H^pm} < m_t +m_b$ that are still consistent with the most recent limits from experimental searches. We find in these regions that, when the $H^pm to W^{pm(*)}h$ decay mode is the dominant one, the $h$ can be highly fermiophobic, with a considerably large decay rate in the $gammagamma$ channel. This can result in the total cross section of the $sigma(ppto H^pm h to W^{pm(*)} + 4gamma)$ process reaching up to ${cal O}(100~{rm fb})$. We therefore investigate the possibility of observing this spectacular signal at the LHC Run II.
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