I'm afraid that there is far too great a temporal distance between the two for you to find a probable link.
Looking for a link between the Illuminati and the Nazis, there are only two possibilities that make sense. Since the Illuminati are assumed to be the present world shadow government and the Nazis lost the war to the current scheme of Illuminati puppets, that would put the Nazis as anti-Illuminati. For the Illuminati to have been controlling the losing side, either they were used as a distraction or lesson to weaken an opposing regime, or they were controlled by an offshoot of the Illuminati in a bid for power.
So now, you have to find a reason that they foresaw either of these scenarios thousands of years ahead and introduced paper money to aid in that endeavor.