I somehow solved the problem.
For each mailbox I use both IMAP and POP. Outlook checks both account (leaving messages on the server through pop).
The default account is an IMAP one so it leaves a copy of the sent items on the server.
The trouble is that if I reply to a message from the main Inbox (which gathers pop only) it uses the pop account and there is no copy of the reply on the server.
I’ll now try to set up a default template that includes a bcc to the sender when replying. Don’t know if it’s possible.