Sooo why do you and @poorquentyn think Benjen left that horn because honestly from a timeline perspective it just never added up. If anything I side more with @Bryndenbfish and go with coldhands. The two biggest flags is the way Ghost was acting prior on the fist and why would Benjen not meetup with the NW and how could he have known there was going to even be a great ranging on the fist of the first men if he was already out there trying to stay ahead of The Others.

As I say in my essay on Jon IV, I think Benjen cached that horn on the Fist because he was being pursued or had to go into hiding. 

To explain your timeline questions: Benjen knew that someone would probably be sent out after him as indeed he had been after Wymar Royce, and the Fist is a natural point for the NW to gravitate to Beyond-the-Wall (hence its use as a rendezvous point for the Shadow Tower and Castle Black during the Great Ranging). 

But to my eyes, the timeline problems are bigger if it’s not Benjen because then he disappears, does nothing, and then suddenly reappears in TWOW.