Large Language Models (LLMs) exhibit a significant "embodiment gap", where their text-based representations fail to align with human sensorimotor experiences. This study systematically investigates whether and how task-specific fine-tuning can bridge this gap. Utilizing Representational Similarity Analysis (RSA) and dimension-specific correlation metrics, we demonstrate that the internal representations of LLMs can be steered toward more embodied, grounded patterns through fine-tuning. Furthermore, the results show that while sensorimotor improvements generalize robustly across languages and related sensory-motor dimensions, they are highly sensitive to the learning objective, failing to transfer across two disparate task formats.