In order to run the ‘New-MailboxExportRequest’ command, you need to run the following first:

New-ManagementRoleAssignment –Role “Mailbox Import Export” –User “DOMAIN\USER”

The ‘New-MailboxExportRequest’ command works after restarting the shell.

New-MailboxExportRequest -Mailbox USER -FilePath “\\SERVER\SHARE\USER.pst”