By mail or through mail

A subtle distinction!

"By mail" typically means that something is sent or received through the postal service, such as a letter or package.

"Through mail" is a less common phrase, but it can also refer to the postal service or a system of communication that uses mail. For example:

In general, if you're talking about sending or receiving something using the postal service, "by mail" is a more common and idiomatic phrase. If you're talking about a system or process that involves mail, "through mail" might be a more accurate choice.