We analyze the cascade decays of the scalar quarks and gluinos of the Minimal
Supersymmetric extension of the Standard Model, which are abundantly produced
at the Large Hadron Collider, into heavier charginos and neutralinos which then
decay into the lighter ones and charged Higgs particles, and show that they can
have substantial branching fractions. The production rates of these Higgs
bosons can be much larger than those from the direct production mechanisms, in
particular for intermediate values of the parameter tanβ, and could
therefore allow for the detection of these particles. We also discuss charged
Higgs boson production from direct two-body top and bottom squark decays as
well as from two- and three-body gluino decays.Comment: 30 pages with 10 figures, latex. Uses axodraw.sty and epsfig.st