This issue will be debated for a long time. However, Henry H. Halley addresses this issue with great clarity. In his book, Halley's Bible Handbook, Zondervan Publishing House, Grand Rapids, Michigan, 113, "There are two leading opinions: Amenhotep II (1450-1420 B.C.), or Merneptah (1250-1220 B.C.). Merneptah was the son of Rameses II, who was a master builder & creator of the Ramesseum, located across the River Nile from modern day Luxor, and the city of Pi-Ramesses. Rameses II, A.K.A. Ramesses the Great or Ramses, is one of the most notable and powerful pharaohs of all time. If Moses was raised by the daughter of Ramses II and Nefertari, then the Exodus occurred under the leadership of Merneptah and the cruel enslavement of the Jews occurred under the leadership of Ramses II. Many scholars believe this based upon the Scripture "Therefore they did set over them taskmasters to afflict them with their burdens. And they built for Pharaoh treasure cities, Pithom and Raamses." Ex. 1:11, KJV.
The International Standard Bible Encyclopedia (ISBE) agrees, but adds that it could have been Amenhotep II. The belief that it was Amenhotep II is somewhat confusing; and yet, compelling! It revolves around Pharaoh's daughter. "If, as many think, the Pharaoh of the Oppression was Thothmes III [a.k.a. Thutmose III, Tuthmosis III, Thutmosis, Thothmes], then Pharaoh's daughter was some unknown princess. Some have thought she was Hatshepsut, the "Queen Elizabeth of Egypt." (from International Standard Bible Encyclopaedia, "Pharaoh's Daughter", Electronic Database Copyright © 1996, 2003 by Biblesoft, Inc. All rights reserved.). Why is it important to determine who the daughter of Pharaoh was? By determining who the Pharaoh's daughter was, we can determine who the Pharaoh was. The problem is tumultuous and I will attempt to explain it below.
By the way, the belief that she was Hatshepsut, the "Queen Elizabeth of Egypt" is also mentioned in Halley's Handbook, p. 112. She was the daughter of Thotmes I. And she was co-regent (co-Pharaoh) with Thotmes II and Thotmes III.
Apparently, Thotmes II married his half-sister, Hatshepsut, who was the real "ruling" power of Egypt. Upon his death, Thotmes III took his place, with Hatshepsut still in power. When she died, Thotmes III extended the empire, built many monuments, constructed a mighty Navy; and is considered the greatest conqueror in Egyptian history.
But, here is where the theory gets confusing. If Thotmes III is the Pharaoh of Moses' time, how could his firstborn son die by the death angel of Exodus? When his firstborn son died two years before? Apparently, Thotmes III, appointed Amenhotep II to be his co-regent two or three years before the Exodus. Thotmes III sent Amenhotep II to lead a battle against the Syrians. So when the death angel swept over the land, it was Amenhotep II's firstborn who died. Furthermore, history records that Thotmes III died in the same year (in the Red Sea).
Hence, the confusion as to whether it was Thotmes III or Amenhotep II who was the pharaoh of Moses' time. It was both. Whose son died? Amenhotep II. And history does record that shortly after his co-regency began, his son died mysteriously.
Thotmes II & Thotmes III were pharaohs during the time of Moses' upbringing. Thotmes III was the Pharaoh during the years that Moses was living in Midian. Thotmes III & Amenhotep II were pharaohs when the Exodus began.
Furthermore, if you take a careful look at the Scriptures, it says in 1 Kings 6:1, "And it came to pass in the four hundred and eightieth year after the children of Israel were come out of the land of Egypt, in the fourth year of Solomon's reign over Israel, in the month Zif, which is the second month, that he began to build the house of the LORD." We only need to trace the time from the fourth year of Solomon's reign and go backwards in time 480 years, you come to the time of Amenhotep II's reign.
Which of the two pharaoh's did Moses oppose? Let the scholars debate that issue. As for me, I believe it was Amenhotep II. After all, it was his son that died! Amenhotep II went to war with the Syrians because he was younger, more virile and did not believe that Moses' threat would amount to a hill of beans.
Could it have been Ramses II? Yes, there is a lot of evidence to show that it was him. It's the timeline that I have a problem with!
The debate will go on and on; but this is for certain, archaeology confirms that the Pharaohs came to power and are now gone, yet the Jews are still living among us. Let God be praised!