For student visas the procedure is slightly different. Letter of invitation from a receiving party (potential employer, business partner or university) should be authorized by Consular Department of the MFA that will fax approval letter directly to the embassy where you plan to obtain your visa. Applicant should get a copy of approval letter (don't confuse it with LOI) from receiving party that they get from Consular Department of the MFA. Approval letter should bear a reference number that you will need to quote in your visa application. Consular Department of the MFA processes LOIs within 3-4 working days.
For visitor visas an invitation is needed from the citizen of Azerbaijan. Invitation has either to be authorized by Consular Department of the MFA (see above business visas) or the applicant can submit a copy of LOI directly to the embassy (without authorization in MFA). The support letter (Devetname) must contain full name of the invited person, his/her date of birth, passport number, duration of stay in Azerbaijan. That LOI needs also to indicate the address and contact details of inviting party. A copy of Azerbaijan citizen's identity document (Shexsiyyet vesiqesi) has to be enclosed as well. However, embassies might still insist on having Letter of Invitation authorized by Consular Department of the MFA, so our advice is to check with the embassy first.