Morphing UVs with Blendshapes

[Parmenides]

How do you morph UV's?  If I take 2 meshes with the same number of verts and different UVs, blendshape ignores the target UV and just stretches it.  When you have text or a distinct pattern this looks awful. 

In the image below I created the mesh  (A), duplicated it and created a new UV (B) then created a blendshape from A to B. 2nd row (L) is the undesired stretched result which should look like the right side.  

[Parmenides · Accepted solution]

Finally figured it out. The missing step was transferring the UVs with 'Mesh/Transfer Attributes'.  Made an explainer for anyone that may be interested:  https://vimeo.com/870508620?share=copy