Wyatt believed Joseph was Imhotep but placed Moses in the 18th dynasty because the chariot wheels he found at the bottom of the Red Sea were thought to date from the 18th dynasty.
There is no evidence for a massive exodus of slaves in the 18th dynasty.
There is a lot of evidence to suggest that the Israelites were enslaved during the 12th dynasty. Moses was born during the co-regency of Sesostris III and Amenemhet III in 1526BC. Moses fled from Amenemhet III at the age of 40 after showing his loyalty to the Hebrews. Moses remained in Exile in Midian for 40 yrs. When he was 80 years old, Moses returned to confront a different pharaoh (Neferhotep I of the 13th dynasty). He lead the Israelites out of Egypt in the 13th dynasty in 1446BC. Pilars were left by Solomon to mark the site of the Red Sea crossing which occurred 480 years before Solomon began building the temple.
Wyatt found these pillars in 1978 and went on to find chariot wheels in the Red Sea at this point. Unfortunately, experts insisted that the chariot wheels could not have been from the 12th dynasty and sent Wyatt on a wild goose chase looking for evidence of the Israelites in the 18th dynasty. There is, however, no evidence for the Israelite slaves and a mass exodus in the 18th dynasty.
The Hyksos exodus at the end of the second intermediate period was not the Israelite Exodus either. The Hyksos were rulers of Egypt. The Hyksos were foreigners to Egypt who were able invade and rule over Lower Egypt after Egypt had been devastated by the Israelite Exodus in the 13th dynasty when Neferhotep was the Pharaoh. The Hyksos ruled Egypt for some 400yrs (Egypt’s second intermediate period). Eventually, the family of Ahmoses based in Thebes (Upper Egypt in the 17th dynasty) contemporary with the Hyksos 15-16th dynasties in Lower Egypt, lead a rebellion against the Hyksos and successfully chased the Hyksos out of Egypt. The Hyksos (Amelekites) headed towards Israel where they had encounters with King Saul and David. The prophet Samuel instructed Saul to wipe them out but Saul spared their king Agag (Apopi II) and brought him to Samuel. Samuel put Agag to death. David had a few encounters with the Hyksos (Amalekites) too. The Amelekites plundered David’s camp and abducted his wives and children. David managed to catch up with them and wipe them out and get his family back. Ironically, it was an Amelakite who slew King Saul after he had been fatally wounded.
In summary, Wyatt seems to have been right about Imhotep being Joseph and did discover the route of the Exodus, the site of the Red Sea crossing and the true or biblical Mt Sinai in Arabia. Unfortunately, the Chariot wheels that he found at the bottom of the Red Sea were erroneously dated to the 18th dynasty which lead him on a wild goose chase looking for Moses in the 18th dynasty. He, nevertheless, made some critical discoveries which have helped to reconstruct history and reconcile it with the Bible.