We consider the exact R-matrix of AdS(3)/CFT2, which is the building block for describing the scattering of worldsheet excitations of the light-cone gauge-fixed backgrounds AdS(3) x S-3 x T-4 and AdS(3) x S-3 x S-3 x S-1 with pure Ramond-Ramond fluxes. We show that R is invariant under a deformed boost symmetry, for which we write an explicit exact coproduct, i.e. its action on two-particle states. When we include the boost, the symmetries of the R-matrix close into a q-Poincare superalgebra. Our findings suggest that the recently discovered boost invariance in AdS(5)/CFT4 may be a common feature of AdS/CFT systems that are treatable with the exact techniques of integrability. With the aim of going towards a universal formulation of the underlying Hopf algebra, we also propose a universal form of the AdS(3)/CFT2 classical r-matrix.