Found Silkworm cocoon, what do do with it?

I found what I believe is a silkworm cocoon. It's white and about 1-1/2" long. It was under my birch tree on the grass, attached to a little stem. I think it's one of those beautiful big moths based on my research. My question is, what can I do with it to "save" the moth? I have it in a jar with holes on the top inside the house, but would it be safe to just leave it outside in my flower bed or somewhere else?