Finally, this add-on it's working back now on Firefox 20 Puntuado con 5 de 5 estrellas
My wait for this add-on to work is over, after the information provided by BlueB on April 7, 2013, there's no need to follow up the drastic solution, provided by afrab_null on April 5, 2013, and the information given by sneekers11 on April 3, 2013, although it was on the right path, it was incomplete and thus, didn't work for me, only the actions presented by BlueB are the correct ones, at least, I get this add-on back to work.
On the provided actions, I only want to mention one point though, which is the "Always use private browsing mode" setting uncheck, if checked, this is part of Firefox Options, Privacy panel, under History, I had the setting "Never remember history", but this doesn't work, since it says that "Firefox will use the same settings as private browsing...", which prevents this add-on to work, the only way that worked for me, was choosing the "Use custom settings for history", which then give the users the possibility to check/uncheck the "Always use private browsing mode" option, on my case, it was checked, and I had to do the opposite action, as mentioned.
Thanks all the mentioned users, for their support. Even with the new working Download Manager on Firefox 20, this add-on is still better than that, it's a "must-have" add-on, and this is confirmed by the use of nearly 2 million users, and the current 7th place, on the "Most Popular" add-ons table, it's incredible how a small add-on, makes a huge difference, regarding download actions, last week, I saw that and I'm glad that everything is working back now!