Setting the Proxy

   Open the Firefox Menu and select Options.
   In the Options window click on the Advanced icon.
   Select the Network Tab.
   In the Connection section click the Settings button.
   Close the Connection Settings and Options windows by clicking on the OK button.

Are you using the Sync feature in Firefox on both of those devices?

That's about the only way that I can think of for any information to get from one device to another without the user purposely transferring that data / those files.

And even if it was thru Sync I could see that image possibly appearing inside Firefox on the Start Page on the other device, but not on the OS Desktop as Wallpaper. And that would need to include another program to divert it to the Desktop; Firefox really only has a contextual menu item to set an image being viewed as the Wallpaper (as I recall, I block that menu item when I set up a new Profile - the contextual menus are too damn long as it is already ...).