So, I'm not sure if this precisely is what prompted your question, but there are a number of websites that say, or suggest, that there were Buddhist communities in Ptolemaic or Roman Egypt, including Wikipedia. This is also a claim that's been made in academic sources, but I'd only ever seen academics citing other people making the claim, and I was curious as to the original source of the claim.Wikipedia's citation for Buddhists in Egypt is based on two sources, and I chased them both up. The citations on Buddhists in Alexandria, or Buddhists as the sect known as the Therepeutai, are from two wildly different sources.
The first is a citation from William Tarn's The Greeks in Bactria and India, which it cites as 1938 but the book was originally published in 1922. This is a surprisingly old citation for such a big deal. When followed up, it's actually Tarn himself citing Flinders Petrie, the famous Egyptologist, from 1898 saying that there were Buddhist gravestones in an archaeological site. Following that up I found the report, actually published in 1900, in which it is recorded that Petrie interpreted one gravestone as having a Buddhist image but both of his fellow excavators disagreed and the inscription on the gravestone suggested nothing of the kind. It seems that William Tarn singlehandedly revived this suggestion without ever referencing the fact that this interpretation was highly disputed, and subsequent academics examining the gravestone in question have never found themselves agreeing with Petrie's interpretation. Were it not for the fact that Tarn's book, which uncritically makes this citation of Petrie, has been republished so many times and is widely available as a full text online, it's highly doubtful this would even have come up.
The second source cited is one Zacharias P. Thundy's Buddha and Christ: Nativity Stories and Indian Traditions, which makes a case that the underlying structure and philosophy of Christianity comes from Buddhism by way of Egypt. I've taken a look at the book and the specific pages cited on Wikipedia. I am entirely confident and comfortable in saying that the work is pseudohistory and totally methodologically compromised, with the passages citing identification of Buddhists in Egypt using no arguments barring deeply questionably etymological assertions, and otherwise the book consists of Thundy telling people what their interpretation is without actually providing any support for it.
These two works seem to be widely cited on several 'mystical' or cryptohistorical websites and I'm almost certain that that's the origin of the claims on wikipedia and the reason for the use of these combinations of source citations in particular, and one should always be suspicious when historical sources quoted on wikipedia are very old and in the public domain.
I am confident in saying that these claims seem to have no supporting evidence with any weight or sound footing, and so unfortunately the answer to that question is that there isn't any known history of Buddhism in Egypt.
There isn't one, or at least its been lost save for a curious relic in a long forgotten desert. If that sounds too dismissive, it is because this a a subject where we have very little to go on and while theories are put forth for there having been Buddhism in Egypt, they are based almost entirely on speculation. But let's look at the facts.
By Alexander's campaigns in the 4th century BCE, Buddhism had spread through the entirety of North India and perhaps even the Swat Valley along with Jainism and Ajivikism (and maybe other Samana traditions like Lokayāta. Historians and philosophers have argued that Alexander, his Generals, and the philosophers (Esecially Pyrrhon) he brought with him must have encountered Buddhism. While the premise seems reasonable, I would doubt that it affected them nor were there any conversions.
Some have noted similarities between Pyrhhon's, who went to India with Alexander, philosophy and Buddhism noting that biographies suggest he was taught in India by "gymnosophists" (naked philosophers) . However the identities of these so called "naked philosophers" is a matter of some debate, most have suggested Jainas as the likely identity, and it is possible some were, others Buddhists, and still others think they were followers of Sañjaya Bellitputta. I personally think that Taxilla being the cosmopolitan center of learning that it was, there was likely a plurality of sects there. In any case Pyrrhon's use of the tetralima and pursuit of serenity through inquiry and knowledge as well as ascetic practices certainly seems Buddhist, but in all actuality predates Buddhist uses of many such techniques. McEvilley argues that Pyrrhon's philosophy had little to do with India but was the result of a long tradition of Greek scepticism and ascetic practices. Regardless, Pyrrhon was not a Buddhist as some more extreme positions have claimed.
There is also speculation that Alexander's teacher from India, Kalanos, who immolated himself upon realisation he was dying and the state would prevent spiritual practise, was a Buddhist. Classically he was considered a Jain, since Digambara Jains do commit ritual suicide and go naked as Kalanos was said to have done, but Jains starve themselves to death and even starting or using a flame violates ahimsa. The suggestion that he was a Buddhist is not so far out as it seems since ritual suicide may have been a feature of some interpretations in pre-secretarian Buddhism. Regardless, I wouldn't say he was a Buddhist for sure and put forth the idea that Ajivika would be a possible identification or perhaps a now lost sect.
All this said, the Greeks appeared not to know the difference between the Samana traditions, but were keenly aware of the divide between Brahminical Orthodoxy and the Samanas. They also appeared to have thought the ascetic practices of Samanas more worthy of respect. To learn more abou the Greeks and Buddhism, I've done a post here.
But why all this talk about Greeks? Well Ptolemy and his successors were Greek and under them Egypt became Hellenised (though it never abandoned classical Egyptian beliefs) as well as a major center for the Silk Road and it's predecessor trade routes between India and the Mediterranean states. Ashoka and the Mauryas seemed to have had some contact with Ptolemy and his successors, if only through Seleucus and his. Ashoka even mentions having sent dhamma-mahamattas (semi-secular ethics educators as part of a policy of universal Dhamma put forth by Ashoka) as far as Macedon and Egypt, though we have no proof they arrived.
It isn't inconceivable that Buddhism had spread to Egypt via trade or Ashoka and the Indo-Greek's missionary activities, but there is no evidence. There is a grave that could be Buddhist in Egypt based on iconography, but this doesn't mean there was a vibrant community of Buddhists in Egypt. The Egyptians, at least the officials, scholars, and maybe traders, were aware of Buddhism in the sense that they knew there were heterodox ascetic sects in India and some people worshiped a person called Buddha, but there is no reliable evidence of a Buddhist presence or community in Egypt currently.
Soureces
McEvilley, Thomas. Shape of Ancient Thought
Robinson, Richard Johnson, Willard. The Buddhist Religion: A Historical Introduction
McKrindle, J. Megasthenes Indika
Tarn, William. The Greeks in Bactria and India
Dhammika, S. The Edicts of Ashoka
Halkias, Georgios. The Self Immolation of Kalanos and other Luminous Encounters...
Basham, Arthur. History and Doctrines of the Ajivikas
Kuzminski, Adam. Pyrrhonism
Beckwith, Christopher. Greek Buddha