First, I would not do the backup over the network. Do the backup local to server A then move it to server B. Since the servers are in different domains, you may need to establish a trust relationship between the domains. I'm not a network or server admin, but if you set the appropriate privledged, you should be able to move the files from server A to server B.
The reason I would do the backup local is if there is any kind of network issue during the backup, it could fail or be corrupted and rendered useless.