Thank you for reading my reply!
Precisely, there is no reputable source that says the phrase is St. Augustine's, as it not on any of his proven writings. It is like another famous phrase ". . . preach the gospel and if everything else fails, use words." It is attributed to St. Augustine but he did not say that. Tony Campolo an Evangelical scholar has written on the phrase, he personally told me that he believed it was St. Augustine's.
Some Church historians, I read somewhere, have attribute it to Martin Luther but I find that really hard to believe because the concept is older than him. Dante had played with the idea in 1308 in the Divine Comedy. (Ecclesia: Pura or Puttana?)
Yet the spiritual concept of the phrase is very strong. It stems from Bible stories like Rahab the prostitute how is redeemed and who later is found in Jesus' genealogy. The prophet Hosea who is commanded by God to mary Gomer a prostitute. Also it is referenced to the whore Babylon which is mentioned in Revelation. Many scholars say this whore, Babylon, is the Church, yet they are not insulting the Church, they are stating a fact followed by the concept of redemption.
The concept is a whore that is turned into saint.
Thank you