Final decisions (that is, the COPR or refusal) are sent by physical mail. Sponsorship decisions are most-often sent by e-mail. If the sponsor received an e-mailed AOR for the sponsorship portion of the application, then the sponsorship approval itself should most likely be e-mailed.
Alternately, you may be able to directly inquire about which visa office is processing the application. Absent the SA/file transfer-letter, you would after all need to know where to send a case-specific inquiry if you had to update documentation.