In the paper we use the theory of framed correspondences to construct Milnor–Witt transfers on homotopy modules. As a consequence we identify the zeroth stable A ¹ -homotopy sheaf of a smooth variety with the zeroth homology of the corresponding MW-motivic complex and prove that the hearts of the homotopy t-structures on the stable A ¹ -derived category and the category of Milnor–Witt motives are equivalent. We also show that a homotopy invariant stable linear framed Nisnevich sheaf admits a unique structure of a presheaf with MW-transfers compatible with the framed structure.