What are the steps to restore an Exchange server database to different Exchange server?
Moving an Exchange Mailbox Database to Another Server or Storage Group
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That depends on the roles the server has been playing, backup systems in place and the state of the 'original' server.
If the server was only handling the mailboxes then you (only) need a full backup of Exchange and restore it on another server.
If the server was also Domain Controller and AD you will have to do a full backup and restore of the entire server.