Personalization of Large Language Models (LLMs) is important in practical applications to accommodate the individual needs of different mobile users. Due to data privacy concerns, LLM personalization often needs to be locally done at the user's mobile device, but such on-device personalization is constrained by both the limitation of on-device compute power and insufficiency of user's personal data. In this paper, we address these constraints by fine-tuning an already personalized LLM with user's personal data, and present XPerT, a new technique that ensure proper selection of such already personalized LLMs based on explainability about how they were being fine-tuned. We implemented and evaluated XPerT on various smartphone models with mainstream LLMs, and experiment results show that XPerT reduces the computation costs of on-device LLM personalization by 83%, and improves its data efficiency by 51%.