I found in the faq the following explanation:
http://www.emclient.com/faq-em-client-features
The Archive button in the main menu appears only for the mail services supporting server-sided Archiving – typically Gmail.
But what means “server-sided Archiving”?
I tried to add a “Archive”-folder to the root of the mailbox as explained in RFC 6154:
https://tools.ietf.org/html/rfc6154#page-3
\Archive This mailbox is used to archive messages. The meaning of an
“archival” mailbox is server-dependent; typically, it will be
used to get messages out of the inbox, or otherwise keep them
out of the user’s way, while still making them accessible.
But it does not activate the button. So what is needed to setup the mailserver activating this feature?