Hi @Kanchana Jayathilake,
Welcome to the Microsoft Forum for technical support.
Based on your description, I would like to explain to you that members of the "Discovery Management" role group in Exchange usually have permissions to perform mailbox searching, but may not have permissions to export mailboxes to PST files. To perform export operations, the "Mailbox Import Export" role is required. This role is not assigned to any role group by default, including "Discovery Management".
You need to add yourself or another engineer to the "Mailbox Import Export" role. This can be done through the Exchange Admin Center (EAC) or the Exchange Management Shell. Here are the instructions for adding a role through the Exchange Management Shell:
New-ManagementRoleAssignment –Role "Mailbox Import Export" –User "Username"
Replace "Username" with the user account you want to grant import and export permissions.
Please feel free to contact me if you have any queries.
Best,
Jake Zhang