  The D3-D5 probe-brane system is holographically dual to a defect CFT which is
known to be integrable. The evidence comes mainly from the study of correlation
functions at weak coupling. In the present work we shed light on the emergence
of integrability on the string theory side. We do so by constructing the double
row transfer matrix which is conserved when the appropriate boundary conditions
are imposed. The corresponding reflection matrix turns out to be dynamical and
depends both on the spectral parameter and the string embedding coordinates.
