I might have it working now. This time I chose to set it up as a new phone then after the phone appeared again in the device list I right-clicked on the iPhone 4S and from the contect menu chose Restore from Backup. This time after the device rebooted it appeared with my iPhone 4's name and started syncing all the apps.
Fingers crossed it completes correctly.
I don't know why it didn't work the first time.