Human activity recognition (HAR) research has increased in recent years due to its applications in mobile health monitoring, activity recognition, and patient rehabilitation. The typical approach is training a HAR classifier offline with known users and then using the same classifier for new users. However, the accuracy for new users can be low with this approach if their activity patterns are different than those in the training data. At the same time, training from scratch for new users is not feasible for mobile applications due to the high computational cost and training time. To address this issue, we propose a HAR transfer learning framework with two components. First, a representational analysis reveals common features that can transfer across users and user-specific features that need to be customized. Using this insight, we transfer the reusable portion of the offline classifier to new users and fine-tune only the rest. Our experiments with five datasets show up to 43% accuracy improvement and 66% training time reduction when compared to the baseline without using transfer learning. Furthermore, measurements on the Nvidia Jetson Xavier-NX hardware platform reveal that the power and energy consumption decrease by 43% and 68%, respectively, while achieving the same or higher accuracy as training from scratch.