There are multiple issues in your file.
To the right of your Source (Cube.001) in your Data Transfer modifier, there's a little button that looks like three arrows. The tooltip for this reads something like, "Evaluate source and destination meshes in global space." By default, this should be enabled; on your image, it is not. If this is not enabled, moving the source mesh around in object mode will do nothing.
Additionally, you're modulating your data transfer by "Face Section" vertex group, but no vertices are assigned to this vertex group.
Finally, you have a subdivision modifier, which by default recalculates your normals. If you'd like this modifier to interpolate existing custom normals instead, enable "Use custom normals" in that modifier's Advanced section.
This is what you're supposed to do-- however, it looks like there's a bug where Blender is failing to create the necessary dependency on the source object. Save and reloading at this point should fix it; adding a subdivision modifier to the source mesh and then deleting that subdivision modifier seems to get Blender to recalculate the dependencies properly.
This will get it working. However, you should be aware that your normals on your source object appear to be backwards. You should probably flip those normals.