You can find special converter utilities (like the ones sold by SysTools) that allow users to explore and recover email messages from Microsoft Exchange Server databases (.edb) and save it to one of the available formats, for example standard Outlook's .pst storage files.
Convert Microsoft Exchange Server Exchange Information Store Database to Microsoft Outlook personal storage table.
We have found one software suitable in our database for this conversion.
Microsoft Windows software - convert edb to pst on Windows
A converter for MS Exchange Server databases
Convert from edb file format
The table with program actions contains information about what each program is capable of doing with their files. This may be a good pointer for further searches for certain file conversions and help you find the converter you are looking for if our search result is insufficient for you. However, it is far from perfect and may sometimes show results which are not really usable because of the nature of the software handles the files. So a conversion that appears as possible, just because of matched actions, may in fact not be possible.