Buying Adobe Illustrator with an invoice

Depending on your region, you might find it easier to work with an Adobe authorized education reseller.

https://adobedealreg.secure.force.com/PartnerSearch?lang=en

There are usually discounts for colleges & unis who buy more than one subscription for their students, faculty and staff members to use.

NB you cannot "buy" it at all, only pay for a continuing subscription, usually with terms of whole years, auto renewed. 

Invoice help https://helpx.adobe.com/creative-cloud/help/print-receipt.html

using a browser that allows popups and cookies, contact adobe support during pst business hours by clicking here, https://helpx.adobe.com/contact.html

click contact us (= cryptic icon in the lower right)

in the chat field, type AGENT
be patient, it can take quite a while to reach a human