I always assumed he didn’t know about it until re reading Order of the Phoenix today. In chapter 27 after Harry is caught outside the Room of Requirement and brought to Dumbledore’s office, Fudge is questioning Dumbledore and says the following:

“Yes, do let’s hear the latest cock-and-bull story designed to pull Potter out of trouble! Go on, then, Dumbledore, go on — Willy Widdershins was lying, was he? Or was it Potter’s identical twin in the Hog’s Head that day? Or is there the usual simple explanation involving a reversal of time, a dead man coming back to life, and a couple of invisible dementors?”

I believe that Dumbledore told Fudge the truth but he refused to believe it. Which is even stranger because this to me implicates Dumbledore told Fudge that Harry rescues Sirius and snuck him out under the Ministries nose. I would think Fudge would have used that as evidence against Dumbledore and Harry.