The connect object is a generator just like Array or SDS Object.
You need to convert it because it’s not exportable.
What happens on Export is that the program converts the object itself, but this changes vertex numbers.
So everything relying on these Numbers will be lost or turn out wrong.
Either combine meshes before adding morphs, or keep them seperated.
You can rig multiple meshes to the same skeleton.
Just make all of them children of the fbx root (null object), rig and weight them to the same skeleton.
You can even have them using different joints of the same hierarchy, e.g. if your head mesh is seperated from the body mesh,
it only needs the joints that should affect it (like head, neck, top of the spine, shoulders, but not arm, hand, fingers, pelvis or even legs).
It might be even better to keep the morphing part a own mesh, since it reduces the ammount of data that needs to be stored for each morph.