[Břicho]

In the Council of Elrond, Gandalf stated that, while the records of Isildur and the Ring had been preserved in Gondor, he guessed that they were unknown to Denethor.

I assume that sometime after sending Boromir off, Denethor might have found the records and figured it out.

It's also possible that Denethor did not know it was the One Ring per se, but figured(as did Faramir) that it must be a thing of great power.

I have never thought that Denethor knew at Boromir's departure that Isildur's Bane was the One Ring.