The short answer to your question is no, Moses is not mentioned in any inscription or papyrus from the time of Ancient Egypt found so far, although he does appear in other ancient historians talking about Egypt. But in understanding the broader scope of Egyptian culture related to history, this absence isn't that surprising.
The Ancient Egyptians were not historians, in any sense of the term we use today. Herodotus, the earliest author of anything we can consider the beginning of unbiased history, lived in a time when the Pharaonic state of Egypt was long gone. Contemporary writings we have from Egypt are almost always in the form of monumental or religious inscriptions, or what papyrus rolls was preserved in tombs. It is akin to understanding the history of the United states based on plaques in the National Mall. Sure, you get very good information on famous rulers, battles, and chronology, but it is always going to be heavily biased to make the kingdom and the dynasty in the best light possible.
On top of that, the Ancient Egyptian religion held a very high, almost mystical reverence towards the use of written language (comes from being the oldest written language in the world). The act of writing things down makes it more real, and more potent, not only for the present but for future generations as well.
For these reasons, the Ancient Egyptians had a taboo against the idea of recording any bad news. Any military defeat for Egypt is spun to sound like a heroic feat, or simply not recorded at all. A famine or plague is only mentioned in the context of the Pharaoh heroically saving the nation. Periods of time when Egypt was subjugated by foreigners are entirely skipped over. Etc. Occasionally, there are works of poetic lamentation from the worst periods of Egyptian history, such as the Admonitions of Ipuwar from the First Intermediate Period, but that's a rare exception. So would the Egyptians leave behind some tablet or inscription how they were plagued and humiliated by Semitic people? Probably unlikely.
After the time of Herodotus, the Pharaohs may have been gone but the culture and written records of Egypt were still very much alive for a long time. Some people who were educated enough were still able to read hieroglyphics until at least the 4th century AD. Thus, a lot of what we know of Egyptian history was first written by Greco-Roman authors during the classical period.
The most famous of these writers is Manetho, whose work is unfortunately lost but can be mostly reconstructed from a variety of fragments. According to Manetho, Moses is described in Ancient Egyptian history as a sorcerer named Musa, and he goes on to identify Aaron and Joshua as well. Manetho likely obtained this information from sources that are now lost.
There was a lot of dispute between the ancient writers, however, as to exactly when the Exodus took place. Manetho himself presented a theory identifying the Exodus as a slave revolt under the reign of Akhenaten. Josephus, a first-century Jewish historian, dismissed that theory and instead identified the Exodus in the reign of Ramesses the Great, and that was the most famous theory for a long time. However, Manetho also describes that a large number of Semitic people were released from Egypt and allowed to return to Canaan in the reign of Thutmose III. So usually Ramesses II and Thutmose III are the two biggest contenders for the Exodus pharaoh, but alternate theories of Biblical chronology can also vary wildly.
u/Antiquarianism discusses the narrative of the Exodus and Moses more specifically here: https://www.reddit.com/r/AskHistorians/comments/gxdy62/was_the_exodus_real/.