Imagine an AI assistant that truly remembers your past interactions, tailoring its responses based on your unique history. This isn't science fiction, but the focus of exciting new research exploring how to personalize Large Language Models (LLMs). LLMs, the brains behind today's chatbots and AI assistants, are impressive but often lack a personal touch. They treat every interaction as a fresh start, forgetting previous conversations. This research introduces PLUM, a novel two-stage pipeline designed to inject the memory of past conversations directly into an LLM. The first stage cleverly transforms conversations into a series of question-answer pairs, essentially creating a 'memory bank' for the LLM. The second stage utilizes a technique called parameter-efficient fine-tuning, allowing the model to absorb this conversational knowledge without requiring massive computational resources. The results are promising. PLUM shows competitive performance compared to existing methods, achieving up to 81.5% accuracy in recalling past conversations. This research opens doors for more natural and less redundant AI interactions. Imagine chatbots that remember your preferences, build on previous discussions, and offer truly personalized assistance. While challenges remain, including managing the balance between remembering specific details and avoiding overfitting, this work lays a crucial foundation for a future where AI remembers and learns from every conversation.