I have an assembly that I am working on that has a lid that transforms from a flat surface to a curved surface:

I want to be able to put this label:

On the flat surface (right under the what-looks-like a hole with nothing in it). The problem is that, in placing the label, half of it would be on the flat surface and half would be on the curved surface.

The end result would look something like this:

This was made by inserting the png image in to the assembly. I want to bring this in as a part - not an image.

I have tried to modify the part by using flex, but it distorts the image.