In one of the podcast episodes of "The Stuff Dream are Made of", one of the hosts mentioned he was bidding on a Darth Vader helmet in an auction a few years back, and later found out the other bidder was Paul Allen. That little tidbit made the rounds in past months, and might be what the recent mention of Allen was from. Otherwise, Paul Allen passed away in 2018. I'm not sure what the status of his collection is now.
[edit]: Some googling turned this up:
“Out of this World” Original Movie Prop Exhibit at The California Museum – High Resolution Photography
So it looks like Paul Allen had a mix of components on the costume that was assembled (at least, as of 2009).