Friendly promotion of one's book on a listserv is perfectly fine, in my estimation. It's a bit self-serving, but that's the way of the world. All book promotions are self-serving, but authors are expected to assist in marketing these days.
However, fishing for reviewers treads a very problematic line, and unabashed solicitation of reviewers for one's own book is utterly beyond the pale. (I believe you erred in volunteering to flog his work for him in BIG Journal X. What would you have done if you found it necessary to write a very negative review?)
If I were you, I would immediately disassociate myself from this unethical adventure in entrepreneurism.
An addendum: Note your language here:
In another later email, editor of Z and author (A) told me that the review had been entrusted to someone else.
The word "entrusted" is supposed to work the other way round.