My experience has been that provided I have "My Poser Stuff" currently loaded as a Poser library, that files saved to it contain correctly formed relative paths.

I appreciate that there may be a problem if you have runtime directly under the root hence my advice to add the "My Poser Stuff" directory and place runtime below that.

I possibly should have mentioned that my texture files are within that runtime, my assumption being that your's were also. If not then they need to be.

Before posting I double checked that this worked. If it works for me my hope was that it will work for you also.

Did you try it?

Suggest creating a "My Poser Stuff" folder and constructing runtime etc folders below that.
Then use the Poser library pallet to add "My Poser Stuff" to it and have that as the current library.
Select the ground plane and apply a texture from within that runtime.
Save the material.

Open the material file in a text editor.
What path format do you see?