Is it possible to publish a map service to a server different to the one where ArcGIS Server was installed? If so, how can this be done?
If you provide the server administrator with an MXD or MSD file, he/she should be able to publish the service from the Manager application on the server you want it to be published to. You may also have to provide any data that the service uses, if the data is not already exposed/available to the server in question.
You will need access to the GIS Server Connection file (.ags) with either an admin or publisher level access to the server in question. This is required in order to publish a service directly to a server. Either they can give you the .ags file directly or give you the user name and password so that you can create one using the following link.
Make note of where you saved the .ags file. Once you have created the file you can use the standard process of publishing a service, simply replace the connection file you would normally use for your server with the new file. Here is a good tutorial that may help you link.
Here is another link to publishing via Python scripting. I choose to go this route if its being done on a semi or regular basis, otherwise once you establish your connection to their server (with the ability to publish services) you can use the desktop wizard. Hope this helps. I can send you an example if needed.