Sensory feedback of grasp forces provides important information about physical interactions between the hand and objects, enabling both reactive and anticipatory neural control mechanisms. The numerous studies have shown artificial sensory feedback of various forms improves force control during grasping tasks by prosthetic hand users through a closed-feedback loop. However, little is known about how perceptual information is transferred between an intact limb and a closed-loop prosthetic limb, and the extent to which training inter-limb transfer may improve myoelectric prosthetic control. We addressed these gaps by using a contralateral force-matching task in which able-bodied participants were asked to generate grasp forces with their native hand, and then match it using the contralateral hand or a soft-synergy prosthetic hand worn on the contralateral arm that was coupled with a mechanotactile feedback device. We found that absolute matching error and matching time were greater when using the prosthetic system than the native hand. However, with contralateral specific training, subjects were able to produce similar relative matching error with the prosthetic system and the native hand, especially at the untrained force level. These findings suggest that an association can be established between the perception produced by the prosthetic limb and the contralateral intact limb, and provide novel insights about potential applications to training and design of the closed-loop prosthesis.