Mobility impairment caused by limb loss, aging, stroke, and other movement deficiencies is a significant challenge faced by millions of individuals worldwide. Advanced assistive technologies, such as prostheses and orthoses, have the potential to greatly improve the quality of life for such individuals. A critical component in the design of these technologies is the accurate forecasting of reference joint motion for impaired limbs, which is hindered by the scarcity of joint locomotion data available for these patients. To address this, we propose ReMAP, a novel model repurposing strategy that leverages deep learning's reprogramming property, incorporating network inversion principles and retrieval-augmented mapping. Our approach adapts models originally designed for able-bodied individuals to forecast joint motion in limb-impaired patients without altering model parameters. We demonstrate the efficacy of ReMAP through extensive empirical studies on data from below-knee amputated patients, showcasing significant improvements over traditional transfer learning and fine-tuning methods. These findings have significant implications for advancing assistive technology and mobility for patients with amputations, stroke, or aging.