Rhino texture mapping on a cone

Hi guys,
I wanna apply a 2D image onto a cone object. The tricky part is the 2D image is an unfolded image rather than a general texture.

I tried to use Spherical and cylindrical mapping but it doesn’t really work.
Is there a way to perfectly project the image on to the object? Or maybe I have to straighten my texture image as a rectangle?

Thanks a lot for your ideas/ help!

can you upload the files to try?

Hi Diego,
Thank you for asking, here’s the 3ds file
cone.3dm (6.9 MB)