With the advent of Industry 4.0, Digital Twin technology has emerged as a pivotal advancement in industrial applications. It enables the creation of a precise digital replica of physical systems. These Digital Twins can be used throughout the entire lifecycle of the physical system, from initial design stages through to operation and disposal. They facilitate design optimization and enable simulations under realistic conditions. This paper presents a case study centered around a UR3e robot, where a Digital Twin is developed using Emu-late3D. Communication between its physical and digital counterparts is established. This setup thus enables synchronized operation: when the physical robot executes a program, the Digital Twin replicates the actions and responses, and vice versa. This represents the first steps towards the use of Digital Twin technology for real-time remote monitoring of the robot.