You can put official on-campus mail in it, and also official outside mail. The university's central mail handling office will add the correct postage and bill your account. Ask your professor. The department also has a Federal Express account. Official airbills with the dept.
Fedex envelopes are in the mail area.
It should not be mailed from the Department mail box. The mail stop is important. Regular-sized mail is put into alphabetical slots. Oversized and bulk mail goes into a series of three large white bins. As the mail gets older it gets dumped into the next bin.