But when retrieving e-mail, it DOES fetch e-mails for the mentioned account.
And also, when sending a new mail, it shows up in the list of from addresses. Notably, it doesn’t have a name set to it, which might be the reason it’s not showing in the account list settings:
If the account is not setup in eM Client, then the application is not connecting to that server to get the messages. Maybe the user has the account forwarded to one they have setup in eM Client.