The likely purpose of the author for introducing the story through Madame Valmonde's point of view was for a well-detailed and true story.
The purpose of Introducing the story through Madame Valmonde or a third person is that a third person can describe the story much better than a person whose life is discussed in the story.
Because Madame Valmonde was the person who grew Désirée up and was there in her life as her parent, she would be knowing more than Désirée about her childhood and how she brought her up in her life.
Therefore, the likely purpose of the author for introducing the story through Madame Valmonde's point of view was for a well-detailed and true story.
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