  The type IIB supergravity AdS_3 x S^3 x T^4 background with mixed RR and NSNS
3-form fluxes is a near-horizon limit of a non-threshold bound state of D5-D1
and NS5-NS1 branes. The corresponding superstring world-sheet theory is
expected to be integrable, opening the possibility of computing its exact
spectrum for any values of the coefficient q of the NSNS flux and the string
tension. In arXiv:1303.1447 we have found the tree-level S-matrix for the
massive BMN excitations in this theory, which turned out to have a simple
dependence on q. Here, by analyzing the constraints of symmetry and
integrability, we propose an exact massive-sector dispersion relation and the
exact S-matrix for this world-sheet theory. The S-matrix generalizes its recent
construction in the q=0 case in arXiv:1303.5995.
