Thunderbird not saving a copy of my sent messages in the "sent" folder

Hi! I am having an issue with displaying sent mails. As you can see in the screenshot (cropped for privacy), I have selected the option to "Place replies in the folder of the message being replied to", which to me means that eg. a reply I sent will both be shown in the "inbox" folder in the message thread, as well as in the "sent" folder. However, it only shows up in the "inbox" folder. Why does this not work?

Thanks!