You'll find the Multiplayer world you want in the main server directory.
You find the folder that has the name that the world you want to put into singleplayer has.
Then, if you have filezilla, right click on the world folder, click download, and it will download wherever you want it to.
If you don't have filezilla, and the server is hosted from your computer, then I suggest you copy and paste the world from the server directory into the Saves folder in the .minecraft folder.
Copy and pasting it is pretty much making a backup, so you don't lose it in your Multiplayer server.

It's not the default world file, it's another one I created with MultiVerse, also the world folder showed up in the SAVES file but not on Minecraft when you click "Single player"

I think you just copy the Region folder from the server folder and put it inside a world that you create in singleplayer, idk just guessing i havent done that yet, ive done a singleplayer world to a server world though..

All you haveto do is open the server folder, and take it world, world is the folder of the save

Ok, thank you, I'll try that next time I'm on my computer, I'll tell you if it worked or not.

Hmm, do you have the server files on your pc (not with filezilla)

If so then just get the world save. Move to desktop and then into saves. Might be a prob with filezilla.