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Replace the default mail function ( $admin = get_bloginfo('admin_email');) of the attached plugin with an admin option to create a list of recipients of the notification emails. The backend of the plugin should display a list of existing site users (admin, editor and so on) along with a check box to select them.
Selected recipients should then receive the notification emails of user submissions. An "Add Recipient" link should display input area to add recipient email id.