I understand (perhaps wrongly) litterae electronicae to be a particular piece of email and cursus electronicus to be the way that email moves around or perhaps the system of networked computers that transmits email. But what is an appropriate word for the thing you check when you "check your email"?
In English, we express this by using "email" as a mass noun (i.e. by omitting the article), but I don't think that carries over to Latin. Perhaps a word for "mailbox" would make the most sense, but the best I've found in Smith's Copious and Critical English-Latin Dictionary is tabellarius publicus, and I'm not sure that makes sense here.