I do not believe Satan transferred sin to Eve that wasn't already resident within her and Adam. Their disobedience was evidence of possessing a sin nature prior to the act. I believe the Enemy did not inject something but rather revealed something preexisting. Eve's disobedience was due to deception, for "Adam was not deceived, but the woman being deceived was in the transgression" (1 Tim 2:14); "the serpent beguiled Eve through his subtilty" (2 Cor 11:3). The evidence of her sin nature was that she saw, "a tree to be desired to make one wise" (Gen 3:6); and we must realize this was before the temptation. These three causes of Eve in Genesis 3:6 have been paralleled with 1 John 2:16; "For all that is in the world, the lust of the flesh (good for food), and the lust of the eyes (pleasant to the eyes), and the pride of life (desired to make one wise), is not of the Father, but is of the world." She was familiar with the fact that "out of the ground made the LORD God to grow every tree that is pleasant to the sight, and good for food" (Gen 2:9), but this scenario did not apply to a tree to be desired to make one wise. Adam's disobedience was due to putting God's word second to his wife, for he "hearkened unto the voice of thy wife" (Gen 3:17). Scripture is not clear concerning Adam's reason for the disobedience, other than "The woman whom thou gavest to be with me, she gave me of the tree, and I did eat" (Gen 3:12). This sounds like blame but I think Adam was just stating a truth, not blaming Eve because my conjecture is that out of compassion for Eve, he was willing to die with her. The crux of this concept is to portray that God in His omniscience "worketh all things after the counsel of His own will" (Eph 1:11); "according to His own purpose and grace" (2 Tim 1:9). Simply put, what transpired was the way He desired it to go, or He would have done it another way.