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Hello  Rémy Friess,
I became curious whne I saw this 9900 mAh battery so I found some tests by several people. I was curious because I use many 18650 batteries and am always looking for something with higher capacity. In short the batteries like the ones you mention tested  at only a fraction of the listed capacity. In all cases they were under 1000 mAh. 
I can only guess that if the 9900 battery is giving you more run time, the original had to be a very bad cell. I think that if you got a  genuine cell from LG, Samsung, Sony or Panasonic/Sanyo rated at 3400 to 3600 mAh you would get better run times than with the 9900 mAh rated cell.
A good one would be the NCR18650G  by Panasonic. But there are others depending on if you need a button top or flat top and with or without  a protection PCB. If you stick with one of the big  4 and buy from a  reputable dealer (does not sell Chinese knockoffs)  you will be much better of than buying no-name batteries with ridiculous ratings from some place like Ebay.

BTW, In this context "genuine" means that actual capacity in real use and/or testing matches what is advertised for the cell in question. for the 9900 mAh battery this is not true, therefor it is not considered genuine.