The story comes from Saint CyrilSource: ADW
Jesus transforms into an eagle in the story
Well then, behold, the night has come, rise and withdraw, and when the morning comes and they accuse me because of you, I shall give them the only son I have so that they can kill him in your place.
Oh Pilate, you have been deemed worthy of a great grace because you have shown a good disposition to me.
It answers some questions raised by the BibleSource: Wikipedia
Then the Jews said to Judas: How shall we arrest him [Jesus], for he does not have a single shape but his appearance changes. Sometimes he is ruddy, sometimes he is white, sometimes he is red, sometimes he is wheat colored, sometimes he is pallid like ascetics, sometimes he is a youth, sometimes an old man.
The powers of Jesus are never fully exploredSource: Wikipedia
Researchers are pretty sure Jesus couldn't shape-shiftSource: Smart History
In Egypt, the Bible had already become canonized in the fourth/fifth century, but apocryphal stories and books remained popular among the Egyptian Christians, especially among monks. I find it difficult to believe that he really did, but some details, for instance the meal with Jesus, he may have believed to have really happened. The people of that time, even if they were well-educated, did not have a critical historical attitude. Miracles were quite possible, and why should an old story not be true?