[Users] Sent mail automatically save to sending folder?

[Brian A]

Is there a way to have mail replies automatically saved to the folder
I'm replying from?  For example an email is received and processed to
folder Home Projects. When composing the reply is there a way to set
the global preference, or account preference config, to save the reply
to the same folder, short of using the "Other" tab in the compose
message reply for each message?

Using IMAP with Yahoo the sent messages are created by
Yahoo in the account's sent folder. Then I go through Sent daily and
sort the messages to the folder where the original message was
processed to start.  My goal is to save that end of day time of sorting
the messages.  I wonder if another processing script on the
account's global Sent folder might do the same trick, but how would
that process get triggered?