Dear Lady helix. Are nautilus descendant of our dear lord helix and you? Thank you and Praise Lord Helix!
To answer your question directly, no, a nautilus
is not a descendant of an ammonite
(both of these are my beautiful bbys)
However, they are somewhat closely related. Within the class Cephalopoda, there are three sublcasses: the Coleoidea (squids, cuttlefish and octopus), the Nautiloidea (a diverse but mainly extinct group, with the exception of the modern day nautilus species) and the entirely extinct Ammonoidea, which of course includes the ammonites, and lord helix himself.
In fact, it is thought that both the Coeloidea and the Ammonoidea are descended from a particular group within the Nautiloidea, kind of opposite to what your question asked!
But like I said, though it’s not apparent today, the Nautiloids were a huge diverse group back in the palaeozoic day, and included not only those similar to the living reclict nautilus species, but also a variety of other forms, including the straight shelled orthocones (which in turn included this huge bastard)
Spiral shelled nautilids and ammonites superficially look very similar, however, there are key differences, for example, the siphuncle (a thread of flesh that runs through the animal’s shell, used growing the shell, and also for controlling water/gass input/output within the shell chambers i.e. controlling buoyancy) runs through the centre of a nautilid shell, as apposed to along the outer edge of an ammonite shell. There are also differences in the number of chambers within the shell, suture shape separating champers, and the fact that ammonites were thought to be able to completely retract within their shells - nautilids (at least living day ones) cannot.
anyway both groups are really super cool and I like cephalopods a lot, I hope that answered your question!