I’m new and started to send a mail to my mailadress from my smartphone. That was OK. Then I tried to send a mail from the eM Client mailbox, but it could’nt send it because an account was missing… What is that about - what account. 

eM Client needs an to have an email account setup in order to send and receive email. In some cases, especially when importing settings from other email clients, either of the send or receiving protocols are not installed.

To check this go to Menu > Tools > Accounts.

There should be an SMTP tab for your account. If there isn’t, scroll down to the bottom of the General tab and tick the SMTP box.