What two items were exchanged before Montag left the professor's house in Fahrenheit 451?
At the beginning of Part Two of Fahrenheit 451, Montag visits Professor Faber's apartment. He takes with him a copy of the Bible, a book which he has illegally kept and which he gives to the professor as a gift. This gift is Montag's way of thanking the professor because the professor agrees to help him to bring down the fireman system by printing copies of books and planting them in the homes of firemen.
As the men are now allies, Faber also gives a gift to Montag: a listening device which looks like a Seashell radio. This is a device of Faber's own design and it will enable the two men to communicate with each other, even though they are not in the same room, or even in the same part of town.
These two gifts symbolize the beginning of Montag and Faber's unlikely friendship and their commitment to bringing about the end of state-sponsored censorship.
After his reunion with Professor Faber, Montag receives a gift of sorts from him in the form of a "Seashell", a tiny device that he can communicate with the Professor through. Using it, he can hear the Professor coach him through his actions, and Faber can hear Montag when he speaks. It is supposed to help them start a revolution in thinking, but things don't quite go as planned.
The other item is a gift from Montag to Faber in the form of a Bible. Montag had rescued it from a house he had been sent to burn, and since it wasn't even known if there were any bibles left in existence, Faber receives it as a treasured gift, and vows to preserve it in the heads of other professors who commit entire books to memory.
When Montag leaves Faber's house, he leaves with a listening and hearing device Faber gave to him so they could communicate when Montag was with Beatty. Montag decides to give Faber the Bible because he knows that Faber knows more about it and appreciates it more than himself.