I have a 650 with a Givi top box. I usually store my helmet in the box when away from the bike. The helmet hanger device on the Burg is very awkward to use and I don't know anyone who uses it. It was designed for a helmet with a "D" ring strap.
I purchased a small "S" shaped snap shackle at Ace hardware. It is stainless steel and was originally designed for use as a key ring. In fact I use a larger one on my belt loop for my keys! When you clip the snap shackle in place on the hanger device (I don't know how else to describe it) all you have to do is clip on your helmet to the shackle and you're done. When you close the seat the shackle and "D" ring is hidden. I think it was about $2.50. Well worth the money.
I purchased a small "S" shaped snap shackle at Ace hardware. It is stainless steel and was originally designed for use as a key ring. In fact I use a larger one on my belt loop for my keys! When you clip the snap shackle in place on the hanger device (I don't know how else to describe it) all you have to do is clip on your helmet to the shackle and you're done. When you close the seat the shackle and "D" ring is hidden. I think it was about $2.50. Well worth the money.