@oratio, there are no such records dating from the time of Ramses or any of the Pharaohs associated with the Exodus story.
The earliest Egyptian mention of the Hebrews—in fact, the earliest mention of the Hebrews anywhere in the archaeological record—is a stele from around 1200 B.C. bragging about how the Egyptian army wiped out a bunch of tribes, including the Hebrews.
I also disagree that it’s just as likely that the Hebrews brought monotheism to Egypt. There is no evidence that the early Hebrews were monotheistic, and plenty of evidence that they were polytheistic. Polytheism is actually preserved in the Bible: Yahweh talks to a heavenly council like Marduk does (he speaks in first-person plural in Genesis, but Hebrew has no royal We). The psalms preserve these battle stories where Yahweh fights the ocean and Rahab and Leviathan. Yahweh says “you shall have no other gods before me”—not “no other gods exist.” Even the idea of a covenant only makes sense in a polytheistic context, since you’re making a deal with a single god to take on the roles of a bunch of gods.
And it’s also telling that Moses (an Egyptian) is cast as the instigator of Hebrew theology in the Hebrew religion itself. Whereas the records we have of Akhenaten say absolutely nothing about Hebrews or any foreign influence whatsoever.
It’s possible — anything is possible — but there’s much more circumstantial evidence pointing the other way.