I have restored and mounted an EDB file onto a new Exchange 2007 Server. However, the old server is still online and although all the mailboxes I need are in the newly-mounted database, in Exchange 2007 System Manager it still shows that the mailbox is associated with the old server.

If I try to "Move" the database it actually tries to copy the files from the old server to the new server, which is not necessary because they are already there - and produces and error about the mailbox on the destination already existing.

How can I simply tell Exchange (AD?) to use the new server to find the mailbox rather than the old?

Edit:

I did the restore by taking the old server offline (turning off all Exchange services), copying EDB file to the new server, restoring it with eseutil, and mounting it to the new server. I did it this way in part because I didn't know a better way and in part because I couldn't use move-mailbox as the source location had a horrible Internet connection (which is why Exchange is being moved to the new location). I had to copy the EDB from the old server to a hard disk, go somewhere with a better Internet connection, upload the EDB to the new server.