How do i change the texture of a material without get it misplaced on the model


I made a low poly-model in blender and used the uv-map there to fit it´s texture perfectly.
The texture is wrapped around the whoole model and as a png-graphic, it looks a bit like a papercraft-printout-sheet for a 3d-model.

than i imported the model as a .dae-file into sketchup to look, how it looks there and and used a special plugin of sketchup to transform one instance of the model into a papercraft-printout-sheet.

Then i had two texture ideas:

For one model i modifyed just a little detail on the texture

For another one, I upscaled the texture until each pixel is stretched into a 16x16 pixel square to make it more look like sharp edged pixels in sketchup.

Then i tried change the texture.
I opened the material, that is asigned to the model to modify it.
There is a text-field to load a texture-graphic-file.

But after changing the texture, it is not more positioned correctly on the faces of the model.

How can i change the texture without changing it´s position on the model-faces?