If someone reads a book review in a journal, they expect that this review reflects an unbiased assessment of the academic qualities of the work in question. The key word here is unbiased.
In your described scenario, it would be the author who suggested that his or her book was reviewed in the first place (+1 potential bias). In addition, the respective reviewer would be one of the author's choosing (+1 potential bias). Finally, the reviewer would be a former collaborator (+1 potential bias).
So, there are three potential points of bias. None of them inevitably has to lead to a biased review: the book might be suitable for a review article in that article anyway, the chosen reviewer might be the candidate anyway that is most fitted for the task, and the final review might be in itself fully fair and objective.
On the other hand, if you suggest your own work for a review article, it might receive more attention than it normally would (and perhaps deserves). If you invite a particular person to write the review, you might be choosing someone who you can assume to agree with your work, perhaps because they work within the same theoretical framework as you do. Researchers from other camps might be less favorable of your book, but they are not given the same opportunity to voice their concerns in their review article, because they never were invited to write one. If the reviewer is one of your former collaborators, they might be more forgiving in their evaluation of your work than actually warranted.
The reader doesn't know that all this is going on behind the scenes. On the contrary, for all what they know, none of the points exist which have the potential of biasing the review, because usually it's not authors who invite reviews, it's not authors who choose reviewers, and usually there should not be a relation between reviewers and authors (at least if the field is large enough). The readers don't expect any of these things, and they therefore cannot take them into consideration when reading and evaluating the review. This is a situation that I consider quite unethical, because information that is crucial for the readers is unavailable to them.
In order to alleviate the situation, you should insist that the review contains a disclaimer which minimally states that the reviewer and the author are former collaborators. In my opinion, it should also reveal that this particular reviewer was suggested by the author.