  We continue our examination of prospects for discovery of heavy Higgs bosons
of natural SUSY (natSUSY) models at the high luminosity LHC (HL-LHC), this time
focussing on charged Higgs bosons. In natSUSY, higgsinos are expected at the
few hundred GeV scale whilst electroweak gauginos inhabit the TeV scale and the
heavy Higgs bosons, H, A and H^\pm could range up tens of TeV without
jeopardizing naturalness. For TeV-scale heavy SUSY Higgs bosons H, A and H^\pm,
as currently required by LHC searches, SUSY decays into gaugino plus higgsino
can dominate H^\pm decays provided these decays are kinematically accessible.
The visible decay products of higgsinos are soft making them largely invisible,
whilst the gauginos decay to W, Z or h plus missing transverse energy (MET).
Charged Higgs bosons are dominantly produced at LHC14 via the parton
subprocess, gb-> H^\pm t. In this paper, we examine the viability of observing
signtures from H^\pm -> \tau\nu, H^\pm -> tb and H^\pm -> W, Z, h + MET events
produced in association with a top quark at the HL-LHC over large Standard
Model (SM) backgrounds from (mainly) t\bar{t}, t\bar{t}V and t\bar{t}h
production (where V=W, Z). We find that the greatest reach is found via the SM
H^\pm(-> \tau\nu) +t channel with a subdominant contribution from the H^\pm(->
tb) +t channel. Unlike for neutral Higgs searches, the SUSY decay modes appear
to be unimportant for H^\pm searches at the HL-LHC. We delineate regions of the
m_A vs. \tan\beta plane, mostly around m_A \sim 1-2 TeV, where signals from
charged Higgs bosons would serve to confirm signals of a heavy, neutral Higgs
boson at the 5\sigma level or, alternatively, to exclude heavy Higgs bosons at
the 95% confidence level at the high luminosity LHC.
