You can control who can export invoices.
To do this, go to Business > Settings > Validation and choose the people in the list. You can multiple select people using the Control key and clicking. Now save your changes.
To appear in this list, the user needs the Finance and Admin role. To provide these roles, head to Admin &Settings and over on the right-hand side, expand the Divisions, find the user and put a tick in the column for these roles.