Steps to reproduce:

1. Load Neutral Base
2. Load 3D Cube prop
3. Attach 3D Cube to the hip bone (or any other)
4. Export as FBX (clothed character). I used Blender profile > Mesh Only
5. Immediately re-import FBX
6. Detach the Cube
7. Try to send the Cube to iClone. Error > Failed to load file

If you try to save the cube as a Prop and load back, the same error pops up in CC

And this is related ticket which is still not fixed in CC4 - none of the UV settings work after Accessory re-import:
https://www.reallusion.com/FeedBackTracker/Issue/Accessories-imported-along-with-Create-Cloth-Hair-Acc-with-FBXKey-loosing-UV-Settings-control

So there must be something terribly wrong with importing accessories attached to Standard CC characters and it just got worse!