In the paper 'Remarks on the conjectured log-Brunn-Minkowski inequality' by C. Saraoglou, the author uses the result (Lemma A. 3.) about the equality case in the Prékopa-Leindler inequality. For the proof the reader is sent to a paper written by S. Dubuc. The paper itself is in French, which I don't know, and the case is more general.
QUESTION: Does anybody know a proof of the equality case of Prékopa-Leindler inequality? Or can say where can I find something (preferably in English).
Thank you.