However it doesn't have anything to do with the story about Jews being enslaved by Egyptians in Egypt however, quite the contrary in fact.
No, it actually does.
The exact piece Amalric is referring to is the victory stele of Pharaoh Merneptah in a mortuary temple in Thebes, relating to a c.1208 campaign against rebels in the land of Canaan. It gives a list of the rebel tribes subdued, including "Israel has been laid waste, bare of seed" (along with others - "Canaan plundered with every sort of woe, Askhelon overcome, Yanoam obliterated, Khor become a widow, etc.")".
The Egyptian conquest of the Levant in the 1450s is (IMO) a much more plausible historical context than the Hyksos a couple of centuries earlier. There was a hug influx of Canaanites into Egypt in the aftermath of the conquest - not merely as POWs from the wars, but also migrants looking for work. Don't forget that the Egyptian state was completely transformed after the conquest - the taxes and tributes from Asia allowed much greater centralization, breaking the pharaoh's dependence on local nomarchs and the creation of a professional Mesopotamian-style bureaucracy and professional standing army mainly composed of foreigners. Levantine migrants - and Canaanites especially - streamed as migrants into Egypt in this era, precisely to serve as highly-skilled craftsmen (formally attached as slaves to temples), to staff the bureaucracy (with their Asian experience) and the army (with new Asian technology, wheel, chariot, etc.). Young Canaanite princes were also brought to Egyptian courts, to be raised and trained in Egyptian mores, and become good loyal vassals when finally sent back to govern their homelands (much like the Romans brought conquered barbarian princes to Rome, etc.) Moses's upbringing would definitely fit the format of one of these princes.
Of course, not all came as voluntary migrants. There were repeated rebellions in the Levantine provinces, which had to be put down by force. And every rebellion would likely lead to the punitive deportation of rebel elements (and maybe tribes wholesale) to Egypt who would likely be put to crappier end of slave work. The victory stele of Merneptah is merely one example of this.
If I had to play speculator, I wouldn't be surprised if Moses was a Canaanite prince of the tribe of Israel (one of many Semitic Levantine tribes), that were taken to be raised in the Egyptian court, that there were long-standing Canaanite migrants serving for generations there already, alongside more recent deportees from Canaanite rebellions. That there might have been a rebellion of the Israel tribe specifically sometime around Moses lifetime (possibly the very one listed in the 1208 stele) which led a mass deportation of rebels to Egypt (just the latest of several waves from prior rebellions), and that the young prince felt it incumbent upon his duty to obtain the release of his tribesmen, availing himself of his court connections and the disorders of the Sea People troubles to return.