Canto 1 - Boyhood
Bāla-kāṇḍa
Chapter 2: Lord Brahmā Instructs Vālmīki
Text 1.2.37

यावद्रामस्य च कथा त्वत्कृता प्रचरिष्यति।
तावदूर्ध्वमधश्च त्वं मल्लोकेषु निवत्स्यसि॥

yāvad rāmasya ca kathā tvat-kṛtā pracariṣyati
tāvad ūrdhvam adhaś ca tvaṁ mal-lokeṣu nivatsyasi

yāvat = as long as; rāmasya ca = of Lord Rāma; kathā = the narrations; tvat-kṛtā = composed by you; pracariṣyati = is propagated; tāvat ūrdhvam = then beyond them; adhaḥ = on earth; ca = and; tvam = you; mat-lokeṣu = among my worlds; nivatsyasi = will reside.

As long as the narration of Lord Rāma composed by you is propagated, you will reside on earth among my worlds and then beyond them.

Since fame is not by itself a goal of human existence, Śrī Brahmā states the result of that fame in this verse. As long as the Rāmāyaṇa is propagated, the sage Vālmīki would reside on earth as long as his body lasts, and then he would live in the world beyond Brahmā’s worlds.1

1 “The world beyond Brahmā’s worlds” is Vaikuṇṭha.