If the author had been given the email address to contact the reviewer about books, then it would be reasonable to use the email address.
Now if the reviewer hadn't specified he wanted informed about new books, then it might be crossing a line.
It wasn't here but another forum and an author noticed I had reviewed his first book. He contacted me out of the blue to review the next one. Note: I wasn't impressed with the first one.
I turned down the offer but it was somewhat awkward.
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