ABJM theory in the presence of a half-BPS domain wall is dual to D2-D4 probe brane system with nonzero worldvolume flux. The was recently shown be integrable lowest order perturbation and bond dimension. In present paper we show that string this integrable, namely boundary conditions on D4-brane preserve integrability Green-Schwarz sigma model. Our result suggests all loop orders for any value

One-point functions of local operators are studied, at weak and strong coupling, for the ABJM theory in presence a 1/2 BPS domain wall. In underlying quantum spin chain wall is represented by boundary state which we show integrable yielding compact determinant formula one-point generic operators.