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 | Autodesk Developer Network
Now we have no “Import Error” anymore…and the Shape Keys works fine