Posture body variation is one of the ways in which humans skillfully and naturally augment their motion and strength capabilities along specific task-space directions in order to successfully perform complex manipulation skills. Posture variation also has a significant role in robot manipulation, where manipulability arises as a useful criterion to analyze the robot dexterity as a function of its joint configuration. In this context, this paper introduces the promising idea of manipulability transfer, a method that allows robots to learn and reproduce desired manipulability ellipsoids from expert demonstrations. The proposed framework is built on a tensor-based formulation of Gaussian mixture model that takes into account that manipulability ellipsoids lie on the manifold of symmetric positive definite matrices. This geometry-aware method is used to design a manipulability-based redundancy resolution that allows the robot to modify its posture so that its manipulability ellipsoid coincides with the desired one. Experiments in simulation validate the functionality of the proposed approach, which extends the robot learning capability beyond trajectory, force and impedance learning approaches.