This　work　is　a　continuation　of　our　previous　work.　In　the　present　paper,　we　study　the　existence　and　uniqueness　of　global　piecewise　C-1　solutions　with　shock　waves　to　the　generalized　Riemann　problem　for　general　quasilinear　hyperbolic　systems　of　conservation　laws　with　linear　damping　in　the　presence　of　a　boundary.　It　is　shown　that　the　generalized　Riemann　problem　for　general　quasilinear　hyperbolic　systems　of　conservation　laws　with　linear　damping　with　nonlinear　boundary　conditions　in　the　half　space　{(t,　x)　vertical　bar　t　＞=　0,　x　＞=　0}　admits　a　unique　global　piecewise　C-1　solution　u　=　u(t,　x)　containing　only　shock　waves　with　small　amplitude　and　this　solution　possesses　a　global　structure　similar　to　that　of　a　self-similar　solution　u　=　U(x/t)　of　the　corresponding　homogeneous　Riemann　problem,　if　each　characteristic　field　with　positive　velocity　is　genuinely　nonlinear　and　the　corresponding　homogeneous　Riemann　problem　has　only　shock　waves　but　no　rarefaction　waves　and　contact　discontinuities.　This　result　is　also　applied　to　shock　reflection　for　the　flow　equations　of　a　model　class　of　fluids　with　viscosity　induced　by　fading　memory.　(C)　2008　WILEY-VCH　Verlag　GmbH　&　Co.　KGaA.　Weinheim.