Who's Got the Horn of Gondor? (Continuity is not PJ's strong suit.)

[Beanamir of Gondor]

I haven't found any other threads that mention this... it's just a minor quibble I have, possibly even just my own confusion on continuity.

During TTT:EE, just before the flashback involving Boromir and Faramir in Osgiliath with their father, we see Faramir sitting in the Window on the West, looking miserable and holding the cloven horn of Gondor. It's quite a moving scene.
But in RoTK, when we first meet Denethor in Minas Tirith, he's holding the cloven Horn of Gondor, and it prompts a Pippin!Flashback. Yet just after Gandalf rescues Faramir's company from the Nazgul, they meet inside the Gates of Minas Tirith, and Faramir says that he saw Frodo and Sam "not two days ago, in Ithilien."

I'm having trouble figuring out whether (a) Faramir stopped in Minas Tirith in the two days between releasing Frodo & Sam, and the retreat from Osgiliath, to drop off the Horn and head out for the battle, (b) it's a continuity mistake, or (c) PJ forgot to tell us about the Gondorian Pony Express, or the magical warping properties of the Horn of Gondor... something like that.

In "The Siege of Gondor", the story is that Faramir had not returned to Minas Tirith since seeing the Halflings... but is there anything about it in the films? Feel free to add any other gripes about continuity.