Minecraft does not provide any support for changing the screenshot folder.
However, you can make a symlink using your Operating System.
If you replace Minecraft's screenshots folder with a new folder, still called "screenshots", that actually links to another location, then Minecraft will unwittingly start saving screenshots in the location you want.
So first, delete the original Minecraft directory screenshots folder (or you can rename it, if you want to save all the screenshots already inside of it without moving them to somewhere else). Then, do one of the following depending on your operating system:
In Windows, you can run this command in cmd.exe (in some versions of Windows you may have to 'Run as administrator'):
mklink /d %APPDATA%\.minecraft\screenshots %UserProfile%\Desktop
On macOS, this is the command:
ln -s ~/Desktop ~/Library/Application\ Support/minecraft/screenshots
Linux is the same as macOS, except the location of the minecraft game directory is different:
ln -s ~/Desktop ~/.minecraft/screenshots
These commands make a new symlink in your Minecraft directory called "screenshots".
After setting up a symlink in your Minecraft directory for screenshots, all new screenshots will be saved to the location that the link points to!