There is a Thunderbird setting for this Puntuado con 5 de 5 estrellas

A per-account setting enables sent email to be immediately enclosed in whatever folder instead of default "Sent"
=> Account settings / Copies & Folders / "When a message is sent, aromatically put a copy in ..." (I'm translating from French layout). This is what I do for each of my accounts in order to have received and sent email all in their Account's Archive folder.

The statement is a bit ambiguous, at least in French, when stated "Put a copy of sent email". At first I thought it would be a copy of the email already in the Sent folder. In fact it means a (the) copy of the sent email itself. Hum... is that English correct ?!

Esta valoración es de una versión anterior del complemento (1.2). 

The feature built into Thunderbird affects where the reply you composed is stored. This add-on affects where the original message (the one you're replying *to*) is stored. Hopefully that clarifies things a bit.