The last we saw of her, Cheryl's body was rapidly decomposing, bursting forth demonic hands, and discharging what looked like to me like cheese grits when Ash managed to toss the Necronomicon into the cabin's fireplace. We might reasonably assume her body continued to break down until there was nothing visibly remaining.
I know what you are thinking, "What, Ash burned the book? How can he have it in his possession now?" That's the thing; the "continuity" among the three films and this series is tenuous at best. The first film involves 5 young people, Ash, Linda (his girlfriend), Cheryl (Ash's sister) and another teenage boy and girl. All die except Ash, though his fate is uncertain as he is seemingly attacked in the last shot of the first movie.
"Evil Dead 2: Dead by Dawn" is in some ways, a sequel. But when it recaps the "highlights" of the earlier film, they are "streamlined" by omitting all characters except Linda and Ash. The events as Ash describes them in this latest episode, Linda's decapitated body dancing in the moonlight, Ash clamping her severed (and still very animated) head in the vise, cutting it with the chainsaw, those are events from ED2. In that film, we don't see him destroy the book (at least, I don't think so).
So, which "version" is correct? That's a good question. Ash talked about "friends", plural, when recounting events to Pablo and we saw footage that showed more people than just Linda. If we were able to "pin down" Sam Raimi, I suspect he'd probably say, "Well, this and this from the first movie happened, but replace these particular sequences with the way they played in the second movie."
It's almost as convoluted as Doctor Who continuity.
Sincerely,
Bill