Heck yes, we're solving those mystery items. Taking some unimportant things from Isengard and Minas Tirith: smoking pipes, medical supplies, maybe some fancypants clothes or things that look both portable and tradeable. Luckily, Aaron's Elvish horse-whispering has left them with mounts, and a stop at Edoras has left them with tack and saddles and other things for taking care of horses.

Boromir gets Anduril.

Faramir gets the Horn of Gondor and possibly the Ring of Barahir.