You should take a backup of the config-store before trying the following workflow.
1. Stop the service of ArcGIS Server (services.msc)
2. Navigate to <Install Drive>\arcgisserver\config-store\services. Locate the folder with the name of the service that you want to copy (*.mapserver)
3. Copy the desired *.mapserver folder and navigate to the desired Folder (inside ...config-store\services). Paste it.
4. Restart the service for ArcGIS Server (services.msc)
Check if the service has moved and running successfully from REST URL or from ArcGIS Server Manager.
Think Location