How to pick texture, but duplicate position, scale, image name and proportions?

Sometimes I hit this problem. I have object with faces. E.g. a cylinder. I have set the inner faces of the cylinder to sky texture.

I have set texture position and scale for the cylinder. For example the name of the material is “sky”. Now I create new material from the “sky” and call it “sky overlay semi-transparent” and I set opacity to 50%. These two materials are identical.

What I need to do now is to duplicate the object; occasionally change it a bit. I need the texture to have the same position and scale, but different material because I set the opacity to 50%.

Now the problem. If I pick the new texture “sky overlay semi-tranparent” it will not have the same values for position and scale. I am not able to fix the texture because the texture is abstract and I do not know the value of the scale and texture to change it manually via measurement if it were even possible (IDK if it is possible to do it).

Here I am lost.

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