Thanks for the suggestions, Kappy. I had not done the original Server installation and was nervous about the possible difficulty of it. But it was not so difficult at all. I installed the Server again and rebooted (without erasing the internal hard drive, which was not necessary); Server started up fine and then I had to configure it. It gave the option of setting up a new server or Restoring from a Time Machine backup,; I chose the latter but it would not recognise the external hard drive on which the TM backup was. So I did a new but minimal Server setup (File Sharing only) with an admin account. Server loaded properly and showed the external hard drive on the desktop. Then I opened Time Machine and the system recognised the old TM backup on the external hard drive. So far, so good. Then I selected the date to Restore files from; it restored files. Then when I restarted, it did not re-start with the Restored system but with the new installation. In a (hidden) Volumes Folder (on the iMac internal drive) I can see the external Drive, a folder called Mac HD (which has all my restored folders), a folder called Mac HD Original (which as all the current startup files), and an alias to the enclosing folder MacintoshHD, which has the files that are being used by the system.
Somehow, I need to get the system to read the Mac HD folder as the system folder. So do you have any ideas how I get the system to read these files as start-up? I can not choose any of these other folders as a startup volume in System Preferences; I've tried to create a disk image of the original files Folder through Disk Utility but the Volumes folder that contains it is not visible to Disk Utility. Again, stumped!