Firstly, if the inner packaging is missing, carefully pad out the Rebo band box with CLEAN tissue paper, plastic bags or bubble wrap (that has no sellotape on it). The band must not be able to rattle around inside the Rebo box during transit and risk damaging either the contents or the Rebo box.
Next, make sure your Rebo Box is well protected on all 6 sides within a very sturdy, significantly larger, preferably double-walled cardboard box. Ideally, you want to allow for the possibility of some delivery monkey puncturing the side of the packing box and still not getting anywhere near the Rebo Band box within, so make sure there's at least a couple of inches protection on all six sides of the Rebo box.
Personally, I hate packing peanuts as they cover everything in dust, so I try to wrap boxed items in tissue paper first (when I have some), but don't sellotape it; there's no need and it risks touching the Rebo box and ripping off some of the litho. Then, bubble wrap the tissue-papered Rebo box (be VERY careful if reusing old bubble wrap to make sure there is no sellotape on it which could damage the Rebo box), then place it in your larger, very sturdy, double-walled box, packing out all six sides with CLEAN paper and or plastic bags and or more bubble wrap and or air bags. Make sure the Rebo box is nowhere near any side of the packing box, and also that it cannot move around within it.
Seal it and post it!