When I create and send a message it is saved in the Sent folder, but when I reply to a message it is not saved in the Sent Folder, although the message does actually get sent. There are no error messages.

I am using the latest version of Thunderbird on a Windows computer. I have no Thunderbird extensions and am using all of the default settings. When I create and send a message it is saved in the Sent folder, but when I reply to a message it is not saved in the Sent Folder, although the message does actually get sent. There are no error messages. I have tried re-installing Thunderbird, compacting each folder, repairing each folder, and turning off my security software, all to no avail. I tried researching the issue but could not find anything that would pertain to this problem. I would appreciate any technical support you can provide. Thank you.