Praise be to Allah.al-hamdu lillaah.
The problem lies in that your friend is a kafir (non-believer) who believes in what the archeologists say more than in what Allaah the Most Exalted says. The only solution is that this friend of yours realizes and believes that the One who created Moses, the magicians, the Pharaohs, and the Persians, knows them better, and knows every minute detail in their lives and all the events that occurred to them, than anyone else. And tell this friend of yours, who claims that he has read the story of Moses and the Pharaoh: Doesnt Allah the Most Exalted say in the Quraan, with regards to the dialogue that took place between Moses and the Pharaoh (interpretation of the meaning): Firaun (Pharaoh) said: " What about the generations of old (previous generations)? Musa (Moses) said : " The knowledge thereof is with my Lord, in a Record. My Lord is neither unaware nor does He forget Verses # 51-52, surat Ta-ha.
We ask Allah to guide your friend to the truth and to reward you for trying to call him to Islam.