If you switch your laptop SSD into the desktop as storage drive ( to store files and documents = NON system drive) while your desktop has it's own system boot hard drive already you don't have to do anything to your SSD.
If on the other hand you're expecting putting your laptop SSD into your desktop and boot from it as it is it's not gonna work, you need a clean install of windows on the SSD to make it work on your desktop as they have different hardware, not to mention windows license/activation issue. ( if you do so you'll obviously loose your laptop windows system).