Which of the following countries was most successful in its economic mobilization for WWII: Britain, the USA, Germany, USSR, or Japan?
This is a very difficult question to answer without detailed statistical analysis. It depends to some degree on what you mean by "success." If you are talking about sheer economic output, then surely the United States was most successful because it was able to produce such huge quantities of war materiel. However, this seems like an inappropriate measure because the US was a much bigger country with much more economic potential than any of the other countries.
I would argue that there is not much to distinguish between the mobilization of Britain, the US the USSR and Japan. Germany was the clear loser.
Germany was a loser because it was not willing to change its society too much in order to put its full efforts into the war. The Nazi regime was not sure enough of the people's loyalty and did not want to resort to such measures as rationing or putting women to work. Germany, therefore, saw very little increase in its GDP as the war went along, even before its production dropped as a result of Allied bombing and other strategic reasons.
The other countries involved, arguably, got everything they could out of their existing economic bases. The British imposed strict rationing on their people and were able to produce large amounts of war materiel as a consequence. Japan did not do as well once the war was under way, but that was largely because it was cut off from its resources by US actions. The US and the USSR saw large jumps in GDP as the war went along.
I would argue, then, that four of these countries really forced their citizens to make sacrifices and put their all into the war. Germany alone was unable to do so.