Neoplatonism outlived its schools by being absorbed into the traditions that displaced it, and its vocabulary is now embedded in places where its name is never mentioned.
In Christianity the transmission runs through two channels. Augustine read Latin translations of Platonic books before his conversion and credited them with freeing him from materialism, and his account of evil as a privation rather than a substance is Plotinian in structure. The second channel is the corpus circulated under the name of Dionysius the Areopagite, the Athenian convert of Acts, now generally dated to around 500 CE. Whoever the author was, he was deeply read in Proclus, and his works transmitted the negative theology, the celestial hierarchies and the language of mystical ascent into Greek and Latin Christianity as though on apostolic authority. Aquinas commented on him; the medieval mystical tradition is unimaginable without him.
In the Islamic world the transmission was partly accidental. An Arabic paraphrase of parts of the Enneads circulated as the Theology of Aristotle, and a compilation drawn from Proclus circulated as the Book of Causes. Both were taken to be Aristotle's, with the result that the Aristotle received in Arabic philosophy, and then in Latin translation from it, arrived carrying a Neoplatonic metaphysics of emanation. Al-Farabi and Ibn Sina built on it; the Latin schoolmen inherited the same mixture, and separating Aristotle from it became a project in itself.
Jewish philosophy absorbed the same currents, visible in Ibn Gabirol and in the structures of Kabbalah, where a series of graded emanations from an unknowable source is the organising idea.
The Renaissance recovered the originals. Marsilio Ficino translated the whole of Plato and then Plotinus into Latin in the later fifteenth century under Medici patronage, and read them as part of a single ancient wisdom running through Hermes Trismegistus, Orpheus and Pythagoras, a chronology that Isaac Casaubon would demolish in 1614. From Ficino the tradition passed to Pico della Mirandola, to Bruno, to the Cambridge Platonists, to Coleridge and the Romantics, and into modern esotericism, where the emanationist scheme and the language of ascent remain in use.