We just started to encounter this situation and checked through the rulebooks and forums and we think we're getting it right but just to be sure :
When we apply a glory hound type power (hehe kill steal) it says "when another character would encounter a monster you encounter it instead". Now we definitely dont have that power yet but there's this armor (forgot the name) that allows us to do the same.
So one char explores, the other steals the encounter. It's a boss and is defeated. Who gets the "when permanently closed" effect? This question didn't crop up before as it was always the char doing the exploring and encounter.
We decided the fellow who defeated the boss. Did we do it right?
I'd say yes. The character doing the encountering is the one that deals with all the ramifications of that encounter. That includes closing.
Applying golden rule #1, i. e. totally supporting Hawk on that view.
Awesome guys thanks! :)