Sure - that was a pain for me too. Without taking it apart to double-super-confirm, here's what I used from the outside in.
barb x 3/8" male thread, brass
3/8" brass ball valve, female threads both ends
3/8" male x 3/8" male, brass (I don't remember the exact length, but it was longer than the shortest thread-to-thread piece)
The white rubber gasket that came with the cooler spigot (on the inside)
3/8" female x 1/2"male, brass
1/2" female x barb, brass
On the outside, I also used a rubber washer, stacked a couple metal washers, and a small section of copper pipe to space things out the right amount and get a compression seal on the inside gasket.
The only reason I converted it to 1/2" on the inside was to accommodate a connection to the circular screen setup in the pic. I would prefer to remove some length from the inside assembly so that the circular screen is better centered in the cooler. Open to suggestions.
Hope this helps.