The biorb filter is in 2 parts. One is the box you describe and the other, bigger part is the rocks on the bottom of the biorb.
Those rocks are the biological media, the main home for the filter bacteria.
The black and white stones - black is carbon, white is zeolite. The sponge is to catch any bits floating in the water. The black & white stones and the sponge will have some bacteria but not nearly as much as the rocks, simply because the surface area of the rocks is so big, plenty of surface for the bacteria to grow on.
Because the carbon, zeolite and sponge in the box are only part of the biorb's filtration system, they won't hold enough bacteria for all the fish currently in the biorb if you use just that in the Juwel filter. To be able to transfer all the fish over, you would have to put all the rocks in the Juwel filter as well as the box, but I don't think there would be enough room for everything.
If you remove the box from the biorb, there should be enough bacteria left in the rocks to keep the fish in the biorb for now, though you will need to keep an eye on the ammonia and nitrite levels till you know the rocks alone are coping - do water changes to remove any ammonia and/or nitrite you might see till the bacteria have multiplied enough to replace the ones in the box.
Once you take the box out of the biorb, put it in the Juwel filter in place of the black sponge. Add ammonia and follow the instructions for fishless cycling.
http
/www.fishforums.net/index.php?/topic/113861-fishless-cycling/
You will need to start adding ammonia as soon as possible after putting the box in the Juwel filter or the bacteria will starve.
Fishless cycling without the box could take anything from four weeks to a few months, but putting the biorb's box in the Juwel filter will give you a head start so the cycle won't take nearly so long.
The reason I said to put the box in the Juwel filter in place of the black carbon sponge is that you don't actually need to use carbon on a routine basis. Keep the black sponge in the cupboard in case you need it at some point to remove medication from the water after treating sick fish.
And don't change the sponges etc like the manual tells you. Wash sponges in the water you take out during a water chnage until they literally fall apart or won't go back to shape after washing. If the filter has cirax, swish that in old tank water and only replace it when the pieces start to distintegrate.
Once the cycle has finished, you will be able to move the biorb fish over.