How can the original surface UV structure be preserved during unrolling?

Having an entirely developable surface and some geometries lying on it (points and curves) I’d like to unroll them all, change these geometries and roll back. I have stumbled across the issue when I roll back the geometries via the Sporth component, those geometries get the wrong position on the original surface. The reason is when the original surface is being unrolled it is losing its genuine UV map. I have tried Rebuild the original surface but it does not solve the problem.

My main goal is to find a reliable method for transforming geometry lying on a developable surface onto its unrolled projection and backward.
Evidently, I have to have the same UV map on both the original and unrolled surface and the question is how to implement this. (588.3 KB)

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You need the Grasshopper equivalent of UnrollSrfUV. I don’t know if it currently exists as a Grasshopper item.