Since he was raised as an Egyptian royal, wouldn’t his signature be Hieroglyphs?
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The Three-Fox-Skins (hieroglyph) is Gardiner's sign listed no. F31, in the series of parts of animals. It consists of 3-fox skins tied at one end, and hanging, creating flowing skins.
In Egyptian hieroglyphs it has the value ms.[1] The word in Egyptian means birth, and related items: to bring forth, produce, fashion, create, etc.
The 3-fox-skin hieroglyph has its origins in the early dynasties of Ancient Egypt, and can be found in multiple usage on the Palermo Stone, (creation or inauguration of events).
https://en.wikipedia.org/wiki/Three_fox_skins_(hieroglyph)
https://en.wikipedia.org/wiki/List_of_Egyptian_hieroglyphs#F
It must have been a three-dog night.
That's a good question.
While hieroglyphics were the formal script of Egypt, used almost exclusively on tombs, memorials, and official documentation, a cursive form called hieratic was used for more practical purposes like record-keeping on papyrus.
I'm guessing if Moses was going to leave a "Kilroy was here" type of inscription out in the middle of nowhere, he would have used this simpler form.