When accessing Outlook Web Access with Firefox, the "Premium" interface (which contains the most features) isn't available. The "Basic" or "Light" interface works in Firefox, but is missing features and may contain bugs. There are no settings or extensions to make Firefox run Outlook Web Access in the same way Internet Explorer does.
Newer versions of Outlook Web Access include better support for Firefox, so you can suggest that the administrators of the site update to the latest version. As a workaround, Windows users can use Internet Explorer to access Outlook Web Access.