Had a game today with the Qax in it. Pretty quickly a debate ensued about whether the person who gets the Qax given to them has to research it again. I ruled that it did, and Blue and Purple half-agreed, but Red was adament that you can give a guy a gun and tell him how to use it without having him discover how it works. (Not the analogy used.) So, what do you guys think?

The card says "once completed..." so i suppose it stays completed/researched for all players. I used it that way, but your question is pertinent and an answer should be included in the FAQ.