What You'll Need
Everything you need to copy, to transfer your world save to your server is found in:
ShooterGame/Saved/SavedArks/
You do not need the entire SavedArks folder.
You will need all of the .arkprofile and .arktribe files. These files contain the information for each Player, and each Tribe.
You will also need your TheIsland.ark (or TheCenter.ark, etc) file (Not any of the TheIsland_TimeStamp.ark files, these are just backups).
You may also want to keep a copy of your game.ini and gameusersettings.ini for reference.
Now to transfer them onto your server, follow these instructions:
1. Login to your account at https://game.auxilex.com
2. Navigate to your server, ensure it is Switched Off, and click File Manager (You can alternatively use an FTP Client for the file transfer, but File Manager will be needed for any extracting of .zip files)
3. Navigate to ShooterGame/Saved/SavedArks
4. Make a backup of any files you want to save here then select all the items in the SavedArks folder, and delete them.
5. Click Upload in the menu bar along the top. Select your files from the other server and upload them.
6. Once the upload is finished, if you need to extract the files, click the extract button.
7. Once all the files listed in the "What you'll need" section are on the server, start the server and verify.