I think that may be changed by adjusting a preference in about:config

Update, in fact I am not sure the name of the preference above is correct, I think it is in in fact browser.download.useDownload.dir

As I said copy any original values before changing them, and be careful about what you do change.

Not sure possibly it works on a rooted mobile.

I don't think that you are able to change this location on mobile.

Posted in an older forum thread:
The download folder is /sdcard/downloads/ there is not currently a way to alter that.

I concur that this location cannot be changed. I've tried. There is no setting "browser.download.dir" in mobile. Even after I added it and put in my phone's sd card location "storage\extSdCard" it did nothing.

I have it working on my S3. These are the steps I followed:

1. Create the Donwload Folder on the external SD card:

  /mnt/extSdCard/Download ( =  /storage/extSdCard/Download)

2. On Firefox about:config:

Create the String value variable browser.download.dir and assign the value of the folder on step 1. It is very important to use the proper caps, so check your folder name and put it here correctly.

3. Modify the variable browser.download.foldelist and set it to 2.

Close Firefox (Kill the app if necessary ) . and that's it!. It worked for me.

This actually works, but the problem is that only images get saved into that SD card directory. If you try downloading a PDF, for example, it still gets saved to the original internal directory. So I would have to say this is a bug.