Does the false prophet cause the spirit of Satan to move into the image to give it life?

It is Satan himself who causes the arising of the beast from the sea, the beast from the earth, the false prophet, and the making of the image. Satan gives rise to those means of getting his wicked will carried out on earth, and he it is who gives them their power and their authority. In chapter 13 of Revelation, Satan is referred to as "the dragon". Here's what the Bible states about the beast from the sea:

"And the dragon gave him his power, and his seat, and great authority. And I saw one of his heads as it were wounded to death; and his deadly wound was healed; and all the world wondered after the beast. And they worshipped the dragon which gave power unto the beast, saying, Who is like unto the beast?" Revelation 13:2-4 A.V. [emphases mine]

Notice that the world of humanity that adores this beast doesn't say, "Who is like unto the dragon?" - no - they think they are worshipping the sea-beast. In all of this Revelation, the dragon - Satan - is invisible. The nations only see the means he uses to deceive them. Here's a shrewd observation about the beast of Revelation 13, showing the link to the various beasts in Daniel chapter 7:

"Daniel's series of beasts combine to give form to the beast of Revelation. What does this signify? In that the beast of chapter 13 incorporates features from all the beasts successively revealed in Daniel chapter 7, besides having features of its own, such a composite implies all those powers envisaged in Daniel, but more. Here is the all-embracing summation of the entire concept, whilst the successive beasts in Daniel depicted manifestations of that concept for the succeeding times then present. But the beast of Revelation 13 answers to time itself...

John stands as it were on the edge of the world. He views time as a whole... John discerns all these beasts as being various successive manifestations of but one. Here is the true vision of the history of the world. John sees one beast, though with seven heads. Of these 'heads', Daniel had envisaged four... John perceives a deeper principle: the heads might have come one after the other, they may have appeared diverse, but behind them all lay one single concept: the beast...

The vision in Revelation is that in which each of Daniel's allegorical beasts in turn became equally incorporated into the one great power lying deeply beneath every single historical materialization of its age-long strife for dominion. These are the seven heads...

But none saw the beast - the eighth - of whom these seven were but the visible successive manifestations.... behind the seven lay the eighth, unknown and unseen but for the Revelation of Jesus Christ given unto the Seer in the vision...

The horn [the beast out of the earth, Rev. 13:11 ff.] is that weapon of thrust and aggression by which a beast asserts its power to slay, subdue, and rule. By the exertion of this force the beast will gain the crown, and by force maintain it. But behind all this lies the dragon, and, in spiritual reality, it is upon his heads that the crowns rest, though it be in appearance by the power of the beast. The mind of the dragon is to gain the crown rights properly due to Christ... Mankind as a whole remains - and will remain - wholly oblivious to what actually takes place in the realm of that which is invisible, spiritual, and visionary." The Revelation of Jesus Christ, John Metcalfe, pp. 307-310

The answer to the question is, in brief: No, it is the other way around. The spirit of Satan is in the various beasts of chapter 13, and the false prophet. The best illustration I can think of is to see the beasts and the false prophet as puppets appearing in sequence on the world stage, and their strings are being pulled by the satanic puppet-master, who always remains out of sight and not even considered by the nations, who are in thrall to the puppets. If they knew that it was the monstrous, great red dragon of Revelation chapter 12 controlling everything and everyone who don't have the seal of God, Satan's game would be up.