The story of what happened to Prahlada after the Narasimha Avatar is narrated to Sri Rama by Sage Vasishta in the Yoga Vasistha.
When Hiranyakasipu (his father), the enemy of all living beings was slain (by Narasimha Avatar of Vishnu) Prahlada became very sad. He thought: "My father and the chiefs of the Asuras have all been annihilated by Vishnu like the Kula Mountains getting destroyed by storms when the world comes to an end. Vishnu has fought many battles with my ancestors. He has never shrunk from fighting. Will he fear me now? I can conquer him only by surrendering to him, by seeking complete refuge with him with all my heart. He is my sole refuge. From this moment I shall take refuge with him. In fact I have already become Vishnu. The mantra Om Namo Narayana fulfils all our wishes. It will never cease to throb in my heart just as air does not in the sky.
Thus Prahlada imagined his body to be that of Vishnu and thought about the proper way of worshipping him. He said to himself: 'Vishnu the Supreme Being exists outside this body in the form of the breath which goes in and out. I shall worship this breath mentally with due ceremony. Accordingly Prahlada worshipped mentally. He next worshipped Vishnu in the temple (within the palace in Patala or netherworld) which contained the actual materials required for worship. Thus he devoutly worshipped the Supreme Lord every day. Following his example his subjects, the Asuras, also began to worship Vishnu.
The news that the Asuras no longer entertained any hatred towards Vishnu and that they had become his devotees reached the heaven. Indra, the king of Devas, and other Devas like the Maruts, Vayu, and Varuna, all were alarmed. They immediately went to Vishnu reclining over the serpent on the Ocean of Milk. They prayed ‘Bhagavan! How is it that the Asuras who were always inimical to you have now become your devotees? What have the wicked and hard-hearted Asuras to do with devotion to you which rises up and develops only in one's last life?'
At this Vishnu said: ' O Devas ! Do not be perturbed over Prahlada's devotion to Me. This is his last birth. He is now fit for Liberation. When a good man ceases to be good it is a sign of danger. But when a bad man turns good it is a good sign. Devas! Return to your abodes. Prahlada's good qualities will do no harm to anyone.' Having said this, the Lord disappeared.
Meanwhile Prahlada was absorbed in his worship of Vishnu. Although he had no desire for sense enjoyment he could not attain peace. His mind was wavering and unsteady. Vishnu knew this by his omniscience and went with his followers to Prahlada's temple in Patala. When Prahlada saw that the Lord had actually come to him he was extremely delighted and worshipped him with greater devotion. With words of great fervor and import he praised the Lord standing before him.
On hearing his words of praise Vishnu was pleased like a peacock at the sight of rain clouds. He said to Prahlada: 'O Precious Jewel of the race of Asuras and their Treasure House! Ask for a boon which will put an end to your birth and death.'
Prahlada replied: ‘Lord, Thou art the fulfiller of all our desires. Thou art for ever omnipresent. Bestow on me the boon which Thou thinkest is the best for me.’
Upon this Vishnu said: O Sinless Soul! Practise Self Enquiry until you attain Brahman and abide in It. Your delusions will come to an end and you will attain the highest good.'
Prahlada thus performed self enquiry and attained Moksha.