That is apparently a matter of some debate.
Not a great source, but there are other letters out there, and at least according to the supposed translation this is among the known ones. The picture shown isn't a match to the fragement shown in the auction.
https://en.wikipedia.org/wiki/Muhamm...heads_of_state
There is a long scholarly work that would indicate that all these letters were discovered within the last 200 years, and that they are probably old forgeries.
https://skeptics.stackexchange.com/q...mmad-authentic
If it is actually a few centuries old, the ink not fading doesn't surprise me. It would have been carbon(Maybe charcoal? ) mixed with some sort of binder. That's been used for millennia, and is still made.
http://www.winsornewton.com/uk/disco...-on-indian-ink