Moon gave the kit to Ringo who gave it to Zak who eventually auctioned it off.
Not getting into the cymbals. Here's some specs for the kit.
It was used around 1975-76. It is a 16 piece kit that was a custom job for Moon. It is a white kit with copper hardware. It consisted of 10,12,13,14,15,16 concert toms. The 15 was specially built for him, as Premier did not offer them at the time. There are also two 22 bass drums, three 14 mounted toms on the basses, two 16 (18deep) floors, and a 18 floor. There is also a set of timbales way up top on the right and a single or a pair of Premier timpani on the left.
The shells are top line and used the African Mahogany plies. This gives them more of a deep and thunderous tone than beech or some other wood used at the time.
Moon used several different snares when he played. This kit was usually seen with Gretsch snares. That is by no means definitive. He liked many many different snare drums.
I am assuming this is the information you were seeking. Hope this answers your questions.