Need help projecting curves on unrolled surface

Good evening everyone, I’m having some troubles trying to use FlowAlongSrf for these blue Curves on the curved surface on the right. I obtained the flat version of the surface by using the Unroll command, then I drew the blue curves and now I want to morph them onto the rounded surface. The problem is that in any way I try I can’t manage to select the whole surface as a target but instead it gets splitted in two parts where that bolder vertical line is on the curved surface. Thanks for your help.

The target surface may be a polysurface, not a single surface. FlowAlongSrf only works with single surfaces.

Upload a .3dm file with the geometry and someone may be able to provide assistance.

also check the help for flowalongsrf,
check this forum for flowAlongSrf, rebuild, unrollSrfUV
unrollSrfUV might give some advantages to be used as base srf