There are some Egyptian sources about the Achaemenid empire. For example, one of the most interesting artifacts from the Late Period in Egypt is the statue of the physician Udjahorresnet, now in the Vatican Museum. The statue describes the invasion of Egypt by Cambyses.

The Great Chief of all foreign lands, Cambyses came to Egypt, and the foreign peoples of every foreign land were with him. When he had conquered this land in its entirety, they established themselves in it, and he was Great Ruler of Egypt and Great Chief of all foreign lands. His majesty assigned to me the office of chief physician. He made me live at his side as companion and administrator of the palace.

Udjahorresnet, perhaps wary of gaining a reputation as a collaborator, was quick to mention his defense of the Egyptian temples under Persian occupation.

I made a petition to the majesty of the King of Upper and Lower Egypt, Cambyses, about all the foreigners who dwelled in the temple of Neith, in order to have them expelled from it, so as to let the temple of Neith be in all its splendor as it had been before. His majesty commanded to expel all the foreigners who dwelled in the temple of Neith, to demolish all their houses and all their unclean things that were in this temple.

When they had carried all their personal belongings outside the wall of the temple, his majesty commanded to cleanse the temple of Neith and to return all its personnel to it... and the hour-priests of the temple. His majesty commanded to give divine offerings to Neith-the-Great, the mother of god, and to the great gods of Sais, as it had been before. His majesty commanded to perform all their festivals and all their processions, as had been done before. His majesty did this because I had let his majesty know the greatness of Sais, that it is the city of all the gods, who dwell there on their seats forever.

At some point Udjahorresnet was sent to Persia, perhaps to tend to the medical needs of the royal court there. We learn that he was sent back to Egypt by Darius I.

The chief physician, Udjahorresne, born of Atemirdis, he says: The majesty of the King of Upper and Lower Egypt Darius, ever-living, commanded me to return to Egypt - when his majesty was in Elam and was Great Chief of all foreign lands and Great Ruler of Egypt - in order to restore the establishment of the House of Life after it had decayed. The foreigners carried me from country to country. They delivered me to Egypt as commanded by the Lord of the Two Lands.

The biography of Petosiris dates slightly later in the Persian occupation of Egypt and hints at more unrest than Udjahorresne was willing to admit.

I spent seven years as controller for this god, administering his endowment without fault being found, while the Ruler-of-foreign-lands was protector in Egypt.

Nothing was in its former place, since fighting had started inside Egypt.

The South was in turmoil, the North in revolt.

The people walked with heads turned back,

All temples were without their servants,

The priests fled, not knowing what was happening.

The copy of the Oracle of the Lamb that survives in P. Vienna D 10000 was copied in the Roman era, but it may have been composed much earlier. Regardless, the text purports to be a prophecy from the 24th Dynasty that predicted Persian and Greek rule in Egypt. "Prophetic" texts written after the fact (ex eventu prophecies) are fairly common in ancient literature. The relevant part referencing the Persians:

However, the Medes will come to Egypt ... judgment will happen to them when they place Egypt...

The prophecy is rather negative, portraying the Persian period as a time of utter chaos.

Many abominations will happen in Egypt. The birds of the sky and the fish of the sea will eat their blood and their flesh, living with respect to them. A man will go to the water... He will not be able to drink or eat in accordance with the book and what is in it. The humble man will bring... He will seize the ... of the great men while he is present though they did not question him. A man will go before his companions; he will say to them what is..., it being in his heart, saying: ‘Who is it?’ A man will go before them to the place of judgment with his companion; they will receive property from the one stronger than them because of the way.

Woe and abomination for the youth, small in age! They will take him away to the land of Syria before his father and mother.

Woe and abomination for the women who will give birth to the youths small in age! They will be taken away to the land of Syria before them.

Woe to Egypt! It will weep because of the curses that are numerous within it.

Moreover, a variety of texts were erected in Egypt by Persian rulers. A statue of Darius was found in Persepolis but was originally erected in Egypt. The statue inscriptions with the titles and boasts of Darius I.

This is the stone statue that King Darius ordered to be made in Egypt in order that anyone who sees it in the future will know that the Persian Man ruled Egypt.

Particularly interesting are the lists of captured territories written in hieroglyphs, including Egypt and Kush, carved into the statue base - literally trampled under the Persian king's foot. This follows a very old Egyptian tradition of listing captured territories; the lists of captured Levantine city-states from the reign of Thutmose III in the 15th century BCE are strikingly similar. The Achaemenid kings were masters of usurping preexisting royal traditions and using them for their own advantage.

The Shaluf stela of Darius I is arguably the most impressive Persian monument erected in Egypt. Like his statue, Darius' stela was multilingual, written in four languages (Akkadian, Elamite, Old Persian, and Egyptian). Originally approximately 3 meters tall and 2.3 meters wide, the stela commemorated the creation of a canal from the Mediterranean to the Red Sea, an ancient precursor to the Suez canal.

A great god is Ahuramazda, who created yonder sky, who created this earth, who created man, who created welfare for man, who made Darius king, who bestowed upon Darius the King the kingdom, great, rich in horses, rich in men. I am Darius the Great King, King of Kings, King of countries containing all kinds of men, King in this great earth far and wide, son of Hystaspes, an Achaemenian. Thus says Darius the King: I am a Persian; from Persia I seized Egypt; I ordered this canal dug, from the river Nile, which flows in Egypt, to the sea which goes from Persia. Afterwards this canal was dug as I commanded, and ships went from Egypt through this canal to Persia as was my desire.