This paper presents a fast and accurate model of a deformable linear object (DLO) -- e.g., a rope, wire, or cable -- integrated into an established robot physics simulator, MuJoCo. Most accurate DLO models with low computational times exist in standalone numerical simulators, which are unable or require tedious work to handle external objects. Based on an existing state-of-the-art DLO model -- Discrete Elastic Rods (DER) -- our implementation provides an improvement in accuracy over MuJoCo's own native cable model. To minimize computational load, our model utilizes force-lever analysis to adapt the Cartesian stiffness forces of the DER into its generalized coordinates. As a key contribution, we introduce a novel parameter identification pipeline designed for both simplicity and accuracy, which we utilize to determine the bending and twisting stiffness of three distinct DLOs. We then evaluate the performance of each model by simulating the DLOs and comparing them to their real-world counterparts and against theoretically proven validation tests.