The observability of a charged Higgs boson produced in association with a W
boson at future muon colliders is studied. The analysis is performed within the
MSSM framework. The charged Higgs is assumed to decay to tb and a fully
hadronic final state is analyzed, i.e., mu+mu- \rightarrow H\pmW\mp \rightarrow
tbW \rightarrow WbbW \rightarrow jjjjbb. The main background is tt production
in fully hadronic final state which is an irreducible background with very
similar kinematic features. It is shown that although the discovery potential
is almost the same for a charged Higgs mass in the range 200 GeV < mH\pm < 400
GeV, the signal significance is about 1sigma for tanbeta = 50 at integrated
luminosity of 50 fb-1. The signal rate is well above that at e+e- linear
colliders with the same center of mass energy and enough data (O(1 ab-1)) will
provide the same discovery potential for all heavy charged Higgs masses up to
mH\pm \sim 400 GeV, however, the muon collider cannot add anything to the LHC
findings.Comment: 18 pages, 11 figure
