This move is based on the Sun in front of the body & is a very clean way of reversing the direction of swing in a sequence of Sun or other moves.
Start the diabolo spinning then swing the diabolo to one side as if to do an Sun in front of the body, but instead of keeping the sticks together hold them apart in front of you as normal. Move the handstick you are swinging the diabolo underneath forward a little way (if you are swinging to your left side, move your left stick forwards). The length of string running from the other handstick should catch on the forward stick & begin to wrap around it.
As soon as the string snags circle the forward handstick underneath the diabolo making sure that the loop of string wrapped around the stick does not slip off of the end. As the diabolo starts to circle down catch it on the length of string running between the two sticks. This should leave the diabolo spinning between the sticks held by a loop.
To exit simply bring your sticks together a little then pull them apart as if to Throw the Diabolo normally. Because the diabolo is also held by a loop of string it forces the diabolo to circle back the way it came over the forward stick & back to the starting position.
Practise this move on both sides & work up to doing continuous stopovers on alternate sticks. As soon as you pull the sticks apart to exit continue the swing straight into a stopover on the other side.
Multiple stopovers
Instead of exiting a stopover straight away, try swinging the diabolo under the same stick again. The longer your string the more stopovers you'll be able to do. You can do lots of stopovers in a row then exit by first throwing the diabolo out as normal then you can keep the movement going by quickly circling the forward handstick causing the diabolo to continue circling round really fast.