When you purchased Win 8 was it an upgrade, retail or OEM? If OEM or retail then yes you can use Win 7 as long as the Win 7 was also not an OEM but retail.
Confusing I know but basically what I'm saying is if the desktop came with Windows 7 preloaded then you can't use it to upgrade the laptop. If you bought Win 7 as retail or upgrade for the desktop then I can't see why you can't use it. As long as the laptop can handle Windows 7.