Significant advancements in contemporary telemedicine applications enforce the demand for effective and intuitive telerehabilitation tools. Telerehabilitation can minimize the distance, travel burden, and costs between rehabilitative patients and therapists. This research introduces an interactive novel telerehabilitation system that integrates the Industrial Internet of Things (IIoT) platform with a robotic manipulator named xARm-5, aiming to deliver rehabilitation therapies to individuals with upper limb dysfunctions. With the proposed system, a therapist can provide upper limb rehab exercises remotely using an augmented reality (AR) user interface (UI) developed using Vuforia Studio, which transmits bidirectional data through the IIoT platform. The proposed system has a stable communication architecture and low teleoperation latency. Experimental results revealed that with the developed telerehabilitation framework, the xArm-5 could be teleoperated from the developed AR platform and/or use a joystick to provide standard upper limb rehab exercises. Besides, with the designed AR-based UI, a therapist can monitor rehab/robot trajectories along with the AR digital twin of the robot, ensuring that the robot is providing passive therapy for shoulder and elbow movements.