Export as OBJ

OBJ files are commonly referred to as Waterfront files.
Importing als OBJ file is not possible with SketchUp freeware, but search on sketchup obj import plugin.

We shall export an OBJ file from SketchUp, import it in Photoshop, edit it there and save it as an OBJ file. And that will be the end of this paragraph, because you can export OBJ from SketchUp Pro, but not import it in Sketchup without the plugin.

Repeat the first steps again but now choose for exporting as 'OBJ File (*obj)'. See the 'OBJ Export Results' panel and click OK.
See above the files that were exported. The MTL file is a so calles Alias file, used in Autodesk. Although you have a folder with the material JPG, the MTL file is also a material file.

Import the OBJ file in a new Phtoshop document.
This works fine. 

To be able to change the material, you now have to click the layer that you see selected here above.
Save as PSD just to be sure.
Do 3D > 'Export 3D Layer' and export it as OBJ.
See all the files you get below here.