Where is "sent" mail saved? To only include what I send as a reply as associated with the initial email is overly simplistic and limiting.
Sent emails should be saved in their complete form in the "Sent" folder. If there is some advantage to maintaining a thread with the original email, then save a concise version of the email in the 'Inbox", but perhaps linked to the full version of the email.
Sent emails are saved in the ‘Sent’ folder in your mailbox.