Since 4.23 you can export finally Shape Keys from UE4 to FBX.
But the Blender Import Script can’t use this FBX Files.
In this example, I use the “Character Customization: Male” Bodymesh.
But if we try to import in Blender we get this Error:
To fix this you must convert the FBX File with FBX Converter (FBX 2013)
The FBX Converter can you download (for free) on Fbx Converter Archives
Now we have no “Import Error” anymore…and the Shape Keys works fine