Thanks for the reply,
Inziladun. You're probably right in your inference. But just because Denethor may have allowed Saruman access to the archives in Minas Tirith doesn't mean that he confided in him. He appears to be a man who kept his own counsel, who listened to people, then made his own decisions.
It was clear from
LotR that he knew who the 'Thorongil' was who lived and worked in Gondor and Rohan in his younger days. What I found interesting was that Faramir, after meeting Frodo and Sam, said that he concluded, from what Gandalf had looked at in the archives concerning Isildur, that the latter had taken something from Sauron before his departure to the North, although he didn't think that it was the Ring until Sam put his foot in it.
My opinion is that his father Denethor had come to the same conclusion.