There’s a bug in Max and FBX export regarding morphs, what you need to do:
1 - save your skin data
2 - Copy your morpher modifer
3 - Delete both modifiers Skin and morpher.
4 - paste the morph back
5 - then apply a new skin and reassign/load all bones data again.
6 -export
The bug comes in when you have skinned the object first and later added the morpher modifer below, FBX expects morpher to be added first and then skinned in that order, for whatever reason.