Transhumeral amputees experience considerable difficulties with controlling a multifunctional prosthesis (powered hand, wrist, and elbow) due to the lack of available muscles to provide electromyographic (EMG) signals. The residual limb motion strategy has become a popular alternative for transhumeral prosthesis control. It provides an intuitive way to estimate the motion of the prosthesis based on the residual shoulder motion, especially for target reaching tasks. Conventionally, a predictive model, typically an artificial neural network (ANN), is directly trained and relied upon to map the shoulder–elbow kinematics using the data from able-bodied subjects without extracting any prior synergistic information. However, it is essential to explicitly identify effective synergies and make them transferable across amputee users for higher accuracy and robustness. To overcome this limitation of the conventional ANN learning approach, this study explicitly combines the kinematic synergies with a recurrent neural network (RNN) to propose a synergy-space neural network for estimating forearm motions (i.e., elbow joint flexion–extension and pronation–supination angles) based on residual shoulder motions. We tested 36 training strategies for each of the 14 subjects, comparing the proposed synergy-space and conventional neural network learning approaches, and we statistically evaluated the results using Pearson’s correlation method and the analysis of variance (ANOVA) test. The offline cross-subject analysis indicates that the synergy-space neural network exhibits superior robustness to inter-individual variability, demonstrating the potential of this approach as a transferable and generalized control strategy for transhumeral prosthesis control.