From a more literary perspective, there’s nothing that directly connects the serpent in the Garden of Eden, the interlocutor in Job, and the later mentions of Satan in the Hebrew and Greek scriptures (and there’s not a lot of direct mentions in the Hebrew scriptures). You can kinda make it work if you read between the lines, but fundamentalists will be the first to say you’re not supposed to read between the lines of the bible. To them, you take the word as it is written and nothing else.
Naturally, this rigid reading of the bible doesn’t work out so well for their beliefs.
To take the Answers in Genesis article on the subject (just because they’re a prominent fundamentalist organization), their reasoning is that the bible shows that Satan can enter into a physical being and control them. Notice that they leave out any reasoning showing that Satan did so in that particular case. He could have, and therefore, he did.