One difficulty in current versions of Thunderbird is that even if you have set the preference to move the signature line related to the quote, it will not be saved correctly.
Luckily there is a way to move this manually. The only problem is that it is a bit of a pain to do so, and if it reverts, you have to make the change manually again. Fortunately it is not hard, just a nuisance.
The first thing you need to do is to exit Thunderbird. This is because the preference is stored in the user.js file. This file, stored in your profile folder, does not exist by default, so you may need to create it (if you have previously created it, or some other preference is stored in it, the file may exist).
If you do not know where your profile is, you may need to do some searching, as this depends on what OS you use for Thunderbird.
Once you have found and/or created the file, you simply need to add a new setting to the file. This setting tells Thunderbird which signature you want to move for which identity you want to move, and looks like this:
What’s that? You don’t know which id to use?
That’s when it gets a bit more complicated. You will need to find your prefs.js file – found in the profile folder – and locate the identity that you want to change. Unfortunately this isn’t the simplest file to browse. It isn’t hard, but you will just need to scroll through it in order to determine which id you are looking for, and once you find it, use that number in the line above. Add it to the user.js file, save and restart.
Note: This article is a bit dated, and may not be valid for current versions. Please keep this in mind.