Let G be a p-adic Lie group associated to associated to a connected reductive group over Qp. Let P be a parabolic subgroup of G and let M be a Levi quotient of P. In this paper, we define a delta-functor H^*J_P from the category of admissible locally analytic G-representations to the category of essentially admissible locally analytic M-representations that extends the Jacquet-Emerton module functor J_{P}.