I have a Pfister widespread bathroom faucet.

As I was working on a leak and replacing the cartridge in one of the handles, I managed to loosen the other handle completely to where this part fell off:

[![Image of part that fell off][1]][1]


It seems that it attaches to the bottom of the handle where the little metal pieces protrude as shown here from the top:

[![Image of part of faucet where thing that fell off should attach][2]][2]


  [1]: https://i.sstatic.net/xQ6ri.jpg
  [2]: https://i.sstatic.net/3M4tU.jpg

When I google, I find a lot of talk about using a basin wrench to tighten plastic nuts, but it seems like this contraption is something else entirely.

Can anyone enlighten me on (i) the names of the pieces and (ii) how I can re-attach the metal part from below the sink and then tighten it somehow?

Thanks!!!