There is a dialog between two persons, and they are discussing some book owned by third person. Which version is grammatically correct: first, second, or both?
To read this book later -- ask John.
To later read this book -- ask John.
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Grammatically, they are both correct. English is very forgiving about the placement of adverbs (see my previous sentence).
However, the emphasis is subtly different. I think a native English speaker might (or might not) use them in different ways.
"This book is freely available for reading now. To read this book later, ask John."
"This book is not available for reading now. To later read this book, ask John."
The difference, in the first case, you have to ask John about "later". If you want to read it now, just go ahead. In the second case, the only way you are going read the book at all is to talk to John. Moving "later" away from "ask" makes it clear that you are getting permission to read it at whatever time available.
However, that's really subtle, and as a practical matter, most native speakers would say, "To read this book later..." in both cases.