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1. Click on the "Add-On Homepage" link at left.
2. Click on the Download link.
3. Right-click on "Download Latest Version (via HTTPS, GitHub), select "Save Link As", and save it.
This will save a file called tabkiller.xpi on your computer. It's a .zip file but your system probably won't recognize it as one due to the extension. You'll have to open the archive using your favorite unzipping program. I recommend 7zip as it is excellent and free.
4. Once you've opened the archive you should see that it contains two folders, a file called chrome.manifest and a file called install.rdf. Open install.rdf using Notepad.
5. Scroll all the way down to the bottom of the text. In the last section you should see a line that says "em:maxVersion="3.7a1pre". Change the "3.7a1pre" to the Firefox version number that you want to use. You probably want to pad it out a little since Mozilla is updating so often. Otherwise you'll just have to do this again later. I used "em:maxVersion="50.0".
6. Save this file. Your archiving program should inform you that the file has been updated and ask you if you want to update the archive as well. Say yes.
7. Run Firefox and click on "File", then "Open File". Select tabkiller.xpi, and it should install normally.