How do you believe consciousness and free will are connected?
The same way as the body is connected to the soul.
I don't know if they are connected, but free-will exists without a conscious mind. My conscious mind has been gone ever since my nervous break-down. I'm on permanent auto-pilot. Hence my previous assertion. So, did I lose my free-will (or just my ability to remember what month and year that it is?). No, my Mind (I swear it is a separate entity) is still making choices. They must still belong to me, even though I don't remember even 15 minutes later having made that choice.
The only freedom any man has is the freedom to think, or not to think, which he can do even in chains, or during "Dark Ages" when he must hide his thinking from the authorities.
The act of thinking is the act of remaining conscious. If you choose not to think, to walk through the world like a zombie and do what you are instructed, or to go along with "community standards" the way Muslims submit to "shura" http://www.alhewar.com/SadekShura.htm then you have given up some amount of your consciousness, and with it the free will that comes from acting upon what your consciousness tells you to do.
If it says "give back the money" and you give it back, that proves you have free will; but so does ignoring your conscience and keeping the money. Choices are what "prove" free will; proves it in your own consciousness as you watch yourself acting on the thought--one way or the other.
There is no free will where a person does what he is told, or what is "expected" of him, or what "god would want" if that is not also what the person wants. Except that if a person acts in that manner and he is not in chains and his mind is active and he can do something other than what he is told or what is expected--then it is his free will to act that way.
"That which you call your soul or spirit is your consciousness, and that which you call “free will” is your mind’s freedom to think or not, the only will you have, your only freedom, the choice that controls all the choices you make and determines your life and your character."
Galt’s Speech, For the New Intellectual, 127.