Let X and X ! be a pair of symplectic varieties dual with respect to 3D-mirror symmetry. The K-theoretic limit of the elliptic duality interface is an equivariant K-theory class m ∈ K(X × X ! ). We show that this class provides correspondencesmapping the K-theoretic stable envelopes to the K-theoretic stable envelopes. This construction allows us to extend the action of various representation theoretic objects on K(X), such as action of quantum groups, quantum Weyl groups, R-matrices etc., to their action on K(X ! ). In particular, we relate the wall R-matrices of X to the Rmatrices of the dual variety X ! .As an example, we apply our results to X = Hilb n (C 2 ) -the Hilbert scheme of n points in the complex plane. In this case we arrive at the conjectures of E.Gorsky and A.Negut from [13].