In this chapter of the Yuddha Kanda of the Ramayana, after Ravana's death his brother Vibhishana is coronated as the king of Lanka:
Hearing the words of the great soled Rama, Lakshmana replied, 'so it be' and rejoicingly procured a golden pot. That mighty Lakshmana, then placing that pot in the hands of the monkey-chiefs, instructed them, who were as swift as thought, to bring sea-water. Thereupon, those excellent monkeys, with the swiftness of thought, moving very quickly from that place, returned, having obtained the water from the sea. Thereupon, Lakshmana together with his friends, taking one pot and making Vibhishana sit on the throne, sprinkled him with sea-water from that pot in accordance with the rule prescribed in Vedic scriptures, while the demons were witnessing the ceremony, to make him the king for Lanka, as directed by Rama. Then, all the demons, as well as the monkeys, consecrated Vibhishana.
And this chapter of the Uttara Kanda of the Ramayana describes how Rama blessed Vibhishana with immortality right before Rama departed the Earth:
He then said to Vibhishana the king of Rakshasas: As long as people shall breathe, O Vibhishana, O highly powerful lord of Rakshasas, thou shalt preserve thy body in Lanka.
But my question is, when and how did Vibhishana step down as king of Lanka? Vibhishana is obviously not ruling Sri Lanka today, so what caused him to stop ruling it?
This excerpt from the Nagara Kanda of the Skanda Puranas describes how when Rama's son Kusha was ruling Ayodhya, he sent a message to Vibhishana to keep the Rakshasas from coming into India and creating havoc. So Vibhishana was still ruling Lanka during Kusha's reign. And going to even more recent times, Vibhishana was still ruling Lanka during the time of Yudhishthira's Rajasuya Yagna, as described in this chapter of the Sabha Parva of the Mahabharata:
And, O king of kings, that slayer of all foes, the virtuous and intelligent son of Madri having arrived at the sea-shore, then despatched with great assurance messengers unto the illustrious Vibhishana, the grandson of Pulastya. And the monarch willingly accepted the sway of the son of Pandu, for that intelligent and exalted king regarded it all as the act of Time. And he sent unto the son of Pandu diverse kinds of jewels and gems, and sandal and also wood, and many celestial ornaments, and much costly apparel, and many valuable pearls. And the intelligent Sahadeva, accepting them all, returned to his own kingdom.
So even during the Mahabharata period, Vibhishana was still ruling Lanka. So what changed between then and now?Do any scriptures describe Vibhishana handing the throne to one of his sons?Do any ancient Indian writers living in the Kali Yuga (like Adi Shankaracharya, for instance) state that Vibhishana was still ruling Lanka in their time?
Now there is a small number of people, like the author of this question, who argue that Ravana's Lanka is not the same as the modern-day island of Sri Lanka. If that's the case then Vibhishana could still be ruling Ravana's Lanka to this day. But I find such theories rather far-fetched.
EDIT: The first chapter of an ancient Buddhist text called the Mahavamsa claims that Buddha went to Lanka and drove away all the Yakshas, which may be a metonymy for Rakshasas, and sent them to a place called Giridipa. And it seems that there was a legendary Buddhist prince named Vijaya who is said to have fought Yakshas in Lanka. But I want to know what Hinduism has to say.