Watch when lone star and dark helmet are fighting and you'll see that lone star drops the ring.Later on when he and barf and the others are celebrating you'll see that he has the ring back.
Lonestar can use the schwartz without the ring. Ever think that he quickly grabbed the ring with it. It is possible. Heck! anything is possible in movies like Spaceballs. That is what is so funny about these movies. Anything can and does happen.
Also, when Lonestar puts Spaceballs, The Shaving Cream (lol) in the guards face and he falls, the ring slips off Lonestar's finger but in the next shot he has it again.