One of the questions that asked frequently – “Is restoring Exchange 2003 database to Exchange 2010 Server is supported?”.
Exchange 2003 & Exchange 2010 databases using the same file extension (.EDB).
However, the schema/format of Exchange 2003 & Exchange 2010 databases is different. Due this, even if you can mount Exchange 2003 database with Exchange 2010 Server, you cant
restore/read the data (New-MailboxRestoreRequest & Restore-Mailbox commands would be failed).
As workaround you can use two options:
Restoring the Exchange 2003 database to a lab environment (e.g. Exchange 2003, with the same service pack level, same Exchange server name, same Exchange organization name, same Active Directory domain name etc.)
Then the database can be recovered to a RSG (Recovery Storage Group) and from there you can export the data by using Outlook/Exmerge tool etc.
Use a third party tool to open the database and export the data to a target mailbox / PST file.