Postfix is an SMTP server. The kind of solution you want (maintaining users' mailboxes) is basically handled by an IMAP server or a local delivery agent.
Only incoming mail (destined for a local mailbox) will be routed to a user's mailbox using a local delivery agent (lmtp, mail.local, postdrop, procmail, etc.).
But making a copy of outbound email and dumping it in the correct user's Maildir ... (which Postfix doesn't know about) .. I don't think so.
That is typically something that's done by an email client over an IMAP session, or by command-line mailreaders like Mutt/Pine, etc., which can also be configured to store sent mail in a specific folder.