The Blue French Horn first appeared in the Pilot episode, in which Ted steals it for Robin after she saw in a restaurant and he said it reminded him of a 'Smurf penis' and she said she'd like one for her apartment. From this point onwards, it can be seen in her apartment on her mantle. When she moves into Ted's Apartment, she keeps it in her room. After moving in with Don, she leaves the horn behind in her empty room for Ted. It is unclear what has currently happened to it, as it cannot be seen in Ted's apartment anymore.
There seems to be an inconsistency in the story, since in Something Blue, Ted says that the restaurant took his driver's license and are keeping it until he returns the horn, and later he and Robin decide to return it to symbolize the end of their relationship. However, it continued appear in Robin's possession, so they could have stolen it back.