Question: Who was the Vizier of  the third pharaoh of the Nineteenth Dynasty of Egypt?

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Vizier (Ancient Egypt): The vizier ( or ) was the highest official in Ancient Egypt to serve the pharaoh (king) during the Old, Middle, and New Kingdoms. Vizier is the generally accepted rendering of ancient Egyptian "tjati", "tjaty" etc., among Egyptologists.  The "Instruction of Rekhmire" ("Installation of the Vizier"), a New Kingdom text, defines many of the duties of the "tjaty", and lays down codes of behavior.  The viziers were often appointed by the pharaoh.  During the 4th Dynasty and early 5th Dynasty, viziers were exclusively drawn from the royal family; from the period around the reign of Neferirkare Kakai onwards, they were chosen according to loyalty and talent or inherited the position from their fathers.

Seti I: Menmaatre Seti I (or Sethos I as in Greek) was a pharaoh of the New Kingdom Nineteenth Dynasty of Egypt, the son of Ramesses I and Sitre, and the father of Ramesses II.  As with all dates in Ancient Egypt, the actual dates of his reign are unclear, and various historians claim different dates, with 1294 BC to 1279 BC and 1290 BC to 1279 BC being the most commonly used by scholars today.

KV13: Tomb KV13, located in the Valley of the Kings in Egypt, was cut and decorated for the burial of the noble Bay of the Nineteenth Dynasty.  An ostraca published in the French Egyptological journal BIFAO in 2000 records that Chancellor Bay was executed by pharaoh Siptah.  Consequently, Bay was never buried in his tomb.  Moreover, no funerary goods were found in the tomb belonging to Bay.  It was later reused by Amenherkhepshef and Mentuherkhepsef of the Twentieth Dynasty.

Prehotep I: The Ancient Egyptian Noble Prehotep I (also known as Rahotep, Parahotep, Prehotep the Elder, Parehotp) was Vizier, in the latter part of the reign of Ramesses II, during the 19th dynasty.

Djau: Djau was a vizier of Upper Egypt during the 6th dynasty.  He was a member of an influential family from Abydos; his mother was the vizier Nebet, his father was called Khui.  His two sisters Ankhesenpepi I and Ankhesenpepi II married Pharaoh Pepi I.  Djau was already in office when his nephew Pepi II became pharaoh.  He is mentioned in two royal decrees, one from Abydos, the other from Coptos; one of them is dated to Year 11.  It is unknown when he died, but when the tomb of Pepi II was decorated, he was no longer vizier.  He was buried in Abydos, but the exact place of his tomb is not known.

KV10: Tomb KV10, located in the Valley of the Kings near the modern-day Egyptian city of Luxor, was cut and decorated for the burial of Pharaoh Amenmesse of the Nineteenth Dynasty of Ancient Egypt.  However, there is no proof that he was actually buried here.  Later, the decoration was replaced with scenes for Takhat and Baketwernel—two royal women dating to the late 20th dynasty.

Ramesses II: Ramesses II (variously spelled also Rameses or Ramses; born ; died July or August 1213 BCE; reigned 1279–1213 BCE), also known as Ramesses the Great, was the third pharaoh of the Nineteenth Dynasty of Egypt.  He often is regarded as the greatest, most celebrated, and most powerful pharaoh of the Egyptian Empire.  His successors and later Egyptians called him the "Great Ancestor".  He is known as Ozymandias in the Greek sources, from a transliteration into Greek of a part of Ramesses' throne name, "Usermaatre Setepenre" , "The justice of Rê is powerful—chosen of Rê".

Intef III: Intef III was the third pharaoh of the Eleventh Dynasty of Egypt during the late First Intermediate Period in the 21st century BC, at a time when Egypt was divided in two kingdoms.  The son of his predecessor Intef II and father of his successor Mentuhotep II, Intef III reigned for 8 years over Upper Egypt and extended his domain North against the 10th Dynasty state, perhaps as far north as the 17th nome.  He undertook some building activity on Elephantine.  Intef III is buried in a large saff tomb at El-Tarif known as Saff el-Barqa.

Nineteenth Dynasty of Egypt: The Nineteenth Dynasty of Egypt (notated Dynasty XIX, alternatively 19th Dynasty or Dynasty 19) is classified as the second Dynasty of the Ancient Egyptian New Kingdom period, lasting from 1292 BC to 1189 BC.  The 19th Dynasty and the 20th Dynasty furthermore together constitute an era known as the "Ramesside period".  This Dynasty was founded by Vizier Ramesses I, whom Pharaoh Horemheb chose as his successor to the throne.

Mehu: Mehu was an Ancient Egyptian vizier who lived in the Sixth Dynasty, around 2300 BC.  The office of the vizier was the most important one at the royal court.  Mehu is mainly known from his monumental mastaba at Saqqara, not far away from the Pyramid of Unas.  The exact dating of Mehu is disputed in Egyptology.  Hartwig Altenmüller published the relief decoration of the mastaba and dates him under king Teti.  He argues that the one of the brothers of Mehu with the name Iynefret is identical to another vizier also named Iynefret, who might date to the early Sixth Dynasty.  Furthermore, Mehu carried the title of an "overseer of priest at Djed-sut-Teti", that is the pyramid complex of king Teti.  Other argue that he dates slightly later under king Pepy I.  Not much is known about Mehu's family.  The parents are unknown.  He has two wives, one called Nebet, the other one Neferkaus.  Mehu was bearing a high number of important titles.  These include the titles of the vizier, but he was also Overseer of the treasuries, overseer of the double granary, overseer of Upper Egypt and overseer of all royal works.  Several sons are mentioned in the tomb.  One son was perhaps called Mery, but his name was several times deleted.  Another son was Hetepka.  Within the mastaba of Mehu there are parts reserved for a vizier called Hetepka.  It is possible that he was the son of Mehu, albeit final evidence for this identification is missing.  The vizier Hetepka might have been just a member of Mehu's family.  Two other known children of Mehu are a daughter called Merut and a further son called Khuy.

Supporting paragraphs: Prehotep I Ramesses II
Answer: Prehotep I