  In this study, we explore the phenomenological signatures associated with a
light fermiophobic Higgs boson, $h_{\rm f}$, within the type-I
two-Higgs-doublet model at the HL-LHC. Our meticulous parameter scan
illuminates an intriguing mass range for $m_{h_{\rm f}}$, spanning
$[1,10]{\;{\rm GeV}}$. This mass range owes its viability to substantial
parameter points, largely due to the inherent challenges of detecting the soft
decay products of $h_{\rm f}$ at contemporary high-energy colliders. Given that
this light $h_{\rm f}$ ensures $Br(h_{\rm f}\to\gamma\gamma)\simeq 1$,
$Br(H^\pm \to h_{\rm f} W^\pm)\simeq 1$, and $M_{H^\pm}\lesssim 330{\;{\rm
GeV}}$, we propose a golden discovery channel: $pp\to h_{\rm f}H^\pm\to
\gamma\gamma\gamma\gamma \,l^\pm\nu$, where $l^\pm$ includes $e^\pm$ and
$\mu^\pm$. However, a significant obstacle arises as the two photons from the
$h_{\rm f}$ decay mostly merge into a single jet due to their proximity within
$\Delta R<0.4$. This results in a final state characterized by two jets, rather
than four isolated photons, thus intensifying the QCD backgrounds. To tackle
this, we devise a strategy within \textsc{Delphes} to identify jets with two
leading subparticles as photons, termed diphoton jets. Our thorough
detector-level simulations across 18 benchmark points predominantly show signal
significances exceeding the $5\sigma$ threshold at an integrated luminosity of
$3{\;{\rm ab}^{-1}}$. Furthermore, our approach facilitates accurate mass
reconstructions for both $m_{h_{\rm f}}$ and $M_{H^\pm}$. Notably, in the
intricate scenarios with heavy charged Higgs bosons, our application of machine
learning techniques provides a significant boost in significance.
