CONTAINS SPOILERS

To fulfill this request to "Deliver Forgotten Desire", first travel to Sapporo Jail. This request mentions an area with nice, clean air and lots of trees around, this is referring to the Arboretum. Enter at the Arboretum checkpoint. Walk behind the checkpoint, down into the building and on the other side you'll find the Forgotten Desire as an item floating as indicated on the map (see image).