You are getting downvoted but this is the traditional history of philosophy as I understand it too (the history of Christianity will be different).
Hellenic culture and texts had permiated Africa and and Mid-east. There were various ancient libraries and academies. Byzantine scholars at the Neoplatonic Academy fled to Persia after it was closed by Justinian. Later in the 8th Century, the Greaco-Arabic Translation Movement gathered books and translated original Greek texts into Arabic at the House of Wisdom (Grand Library of Baghdad). Study of hellenic philosophy restarted in the Arabic world until the Golden Age of Islamic Philosophy with Averroes whose commentarities reintroduced Hellenic philosophy to Europe in the 12th century.
I don't think that particular flow needs any Irish Monks but <shrug> I don't know the specific sources of books used by the Translation Movement.
The monasteries of Ireland and Scotland survived the crisis and disorder of the Migration Period and re-christianized the Continent from the 8th century onwards. Yes, some texts from antiquity have come down to us only as palimpsest, but the classical writers were copied.
The works of Aristotle were translated from Greek to Arabic by Islamic scholars in the early Middle Ages, mostly pre-dating the Latin translations, and they were sometimes the source from which the Latin translations were made.
Greek Orthodox; Roman Catholics forgot Greek. Until Marsilio Ficino translated Plato to Latin around 1450, Plato had been effectively lost in the west for 1000 years.
A lot of those scholars were not "Islamic" or "Muslim", just happened to live in the area. Many of them were christians (Church of the East), Sabians, Jews, or local hellenistic inspired cults. Also some of those translations were translated to other local languages (eg. Assyrian, Hebrew...) then to Arabic.
Of course, in todays world, one could say Arabic/Islam becoming the dominant culture/religion minimized the work and exposure others get.
