Copy dovecot mail files from backup back into user’s mailboxes

Following on from our comments above, the problem seems to be SSL/TLS-related. You tell me that the client having problem isn't configured to use either SSL or TLS, but in the dovecot -n output in your question, the line

ssl = required

appears. I suspect that when the client connects on the plaintext service (port 143), the daemon, being configured to require encryption, promptly tries to engage TLS. Since the client's not configured for that, it ignores the attempt to uprate security, leading to the server getting frustrated and dropping the connection with the log error

TLS handshaking: Disconnected

Postfix should be enough to this scenario. Check the sender_bcc_maps and recipient_bcc_maps feature. As documented, two parameters defines an mapping where copies of particular mail account handled by postfix are sent to.

Assuming that your mail account is user@example.com and you want to copy it to external@example.net.

sender_bcc_maps = hash:/etc/postfix/special_user
recipient_bcc_maps = hash:/etc/postfix/special_user

In /etc/postfix/special_user add this line

user@example.com    external@example.net

Don't forget to postmap the map file and run postfix reload