Thanks for updating us.
Does the same problem occur with any character you export to FBX or is it just this particular character?
Also, do make sure that you have iClone 7 and 3DXchange 7 Pipeline updated to the latest versions. That is 7.41 for iClone and 7.4 for 3DXchange 7.
You should also make sure you have your graphics drivers are updated as these kinds of issues can often be driver related.