sieve filter generated email- sent folder

dovecot 2.3.21 pigeonhole 0.5.21. Filters created via roundcube.

Attempting to have filters detect certain email, send a notification text message to mobile via email, and copy that notification email to "Sent" folder.

Filter(s) detect condition, move the email to desired folder and appear, as note in logs outside of dovecot, to sent the notification email. The notification email is not recorded in "Sent" folder and is not received by mobile device.

Is this a "do-able" thing in dovecot/pigeonhole?

If so, how? Docs available?