Get to know your fan and understand it's directionality and the polarity of your 12V adapter so you can be sure your are facing the fan the correct direction when you glue it into the leftover container part of your home-made dryer duct adapter. Strip the ends of the leads and conntect them to your power adapter. If the fan doesn't run at first, reverse the leads on the adapter, as polarity seems to matter on these fans. Face the fan so that it will blow OUT of the the can side of the duct flange. Cut a small slit in the side of the container closest to the wire leads for the fan and pass them through. Use four generous blobs of hot glue and press and hold the fan firmly in place until the glue hardens. Use another blob of hot glue to seal and secure the wire leads passing through the container. Strip the leads of both the power adapter and the fan. Twist connections and wrap with electrical tape. Tie a knot in the wire above the wire splice to provide stress protection in the cord.
This will help If & When you ever move to another house.