Let us suppose that we have received a rejection of our paper form a journal, but this rejection contains a really very valuable and detailed review, so some ideas of this review after some consideration and rethinking will be included into the new version of the paper.

And I here have two questions. No doubts: the new version of paper will contain acknowledgements to the anonymous reviewer. But:

  1. Is it a good manner to answer editor's rejection letter and ask him to pass our deep appreciation to the anonymous reviewer?

  2. Is it somehow possible to ask the editor to pass our desire to invite this reviewer to be a co-author of our paper?

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    Yes and yes. Keep in mind that sometimes a reviewer might pass on your offer in order to maintain his/her identity. – The Guy Jul 20 '17 at 11:59
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    @TheFireGuy thank you for your comment! Why not post it as an answer? :-) – user70829 Jul 20 '17 at 12:00