In the very broadest sense, the video is correct - as Byzantine Egypt was divided between different factions, an army of Muslims under Amr invaded and quickly conquered the province within a few years. However, I looked at his other videos briefly and it looks like the creator has an... interesting take on history. Columbus for instance apparently sailed west to try to find an alternate way to Jerusalem, and a few other videos have titles like 'Muslim Cannibals of the Crusades' and 'Rick Santorum Gets the Crusades Right'. He is definitely not an impartial historian and I get the impression he might be pushing some sort of anti-Islamic agenda.

So what really happened during the conquest of Egypt? Our best source is John of Nikiu, a late-seventh century Coptic monastic administrator who wrote a universal chronicle that ended with the Arab Conquest. He was clearly quite knowledgeable about recent Egyptian history and his material is generally more trusted than later, more extensive Islamic accounts (which were compiled from oral accounts only in the mid-eighth century). The problem is that his chronicle is confusingly organised and its English translation unbelievably shoddy (you can read it for yourself here). Moreover, A.J. Butler's book on the conquest of Egypt, published more than a century ago, is still the most extensive account of this campaign, which is obviously problematic.

As the video says, in 639 Amr and a small force invaded Egypt, however, the war cannot be simplified down to Amr attacking walled cities and massacring inhabitants. Both J. Howard-Johnston and P. Booth have recently suggested that the conquest occurred in a round-about fashion. In Booth's telling, there were multiple armies and one army followed the coast south and then attacked from the Upper Nile, effectively attacking from behind Byzantine defences, whilst Howard-Johnston suggested that Amr launched an attack on Oxyrhynchus and cut Egypt in two. In either case, Amr was an astonishingly good general and he should be praised for his generalship. A truce was made under Cyrus, the Chalcedonian Patriarch/effective governor of the province, to evacuate Byzantine forces from threatened areas, but the emperor Heraclius wanted his armies to fight rather than to peacefully hand-over Egypt, so Cyrus was removed. Heraclius died in 641 and his successors abjectly failed to defend their eastern possessions because of infighting between his sons Constantine III and Heraklonas. The former died within months, but court intrigue quickly removed Heraklonas and placed Constantine III's son, Constans II, on the throne. Constans was only 11 in 641, so I doubt he actually did anything... instead, it was the regency government who oversaw the Byzantines' final defeat in Egypt and the failed expedition of 645/6.

The second issue I have with the video is his emphasis on the destruction wrought by the Arabs. Some massacres probably occurred, but like in many places during the Arab Conquests, many settlements simply surrendered. Partly this was because the Muslim armies generally offered a good deal, that is if the citizens pay a lump sum, they will not be harassed. Specifically in Egypt, there were also tensions between the Chalcedonian Church, which became monothelete in the 630s (and thus heretical even to some Chalcedonian Christians), and the Coptic Church, which was miaphysite. There were effectively two opposing Patriarchs of Alexandria in the late 630s, Cyrus for the Chalcedonians/monotheletes, and Benjamin for the Copts. Cyrus rigorously persecuted the Copts to get them to follow the official line, with many people, including Benjamin's brother, being martyred. No surprise then, when a relatively tolerant enemy arrived, many Copts did not resist as hard as they could have. There is also some evidence that they actively co-operated with the Arabs, though I don't have Butler's book on hand so I can't talk about how extensive that was. Remember also that less than 20 years before this campaign, the Persians had also occupied Egypt and were quite generous to the Coptic majority of Egypt - loyalty to the Byzantine state, the great persecutor the Copts, was definitely not at an all-time high! There is a recent suggestion by P. Booth that the persecution of Copts may be exaggerated by later Coptic sources though, as they might be trying hide the miaphysites' 'shameful' agreement to an earlier Union with the Chalcedonian Church, but I'm not sure how convincing this is.

Anyway, the comment that everyone in Nikiu was killed is evidently false, since John of Nikiu was part of the next generation. Plus, Late Antique authors tend to exaggerate, so the video-maker/old-fashioned histories he used should not have trusted the sources so naively. More generally, from sources such as John of Nikiu, the Coptic History of the Patriarchs of Alexandria (a regularly updated history of the Patriarchate) and prosopographical evidence, we know that administratively, Egypt was still divided the same way and that many local headmen/overseers continued in their positions post-Conquest. Egypt was not ruined and under Muslim rule, the province continued to be a massively productive one. Muslim rule was not entirely pleasant of course, since we have evidence of tax riots, mass desertions and general oppression - then again, Byzantine Egypt was similarly unstable, so we can't judge the Muslims too harshly for their inability to govern a socially-divided province. Interestingly, John of Nikiu criticised Cyrus and various Byzantine turncoats (evidently, Byzantine governors were not automatically removed!), but Amr received a much more positive treatment - Amr apparently removed an ex-Byzantine governor who raised taxes and imposed another ex-Byzantine official who lowered them instead. It may be that John couldn't write anything negative about Amr under Muslim rule, but more likely, given how Christians were often involved at the highest level of Islamic government throughout the Middle East, Amr was indeed a relatively peaceable ruler. Some later governors during the Umayyad period were harsher, and it has been suggested that it was during this period that the Coptic History of the Patriarchs was partially rewritten, in order to remove earlier accounts of Arab-Copt co-operation - I'm not an expert on this specific source, so I can't tell you any more I'm afraid! This quote from John of Nikiu says it all though:

[After the conquest] Abba Benjamin, the patriarch of the Egyptians, returned to the city of Alexandria in the thirteenth year after his flight from the Romans, and he went to the Churches, and inspected all of them. And every one said: 'This expulsion (of the Romans) and victory of the Moslem is due to the wickedness of the emperor Heraclius and his persecution of the Orthodox through the patriarch Cyrus. This was the cause of the ruin of the Romans and the subjugation of Egypt by the Moslem.

Let me know if you have any questions! :)