To my knowledge, there are no large scale studies done looking at whether coconut oil helps with Alzheimer's, but there is enough anecdotal evidence that a study is being done at the University of South Florida's Byrd Alzheimer's Institute. The Doctor who has collected 275 anecdotal cases, including that of her husband, is Mary Newport. Her husband responded so dramatically to taking coconut oil that she wrote a book about it, which you can see here:
How or why can coconut oil potentially help with Alzheimer's? Coconut oil provides fuel to the body's cells in the form of ketones. The cells of the brains of people with Alzheimer's apparently cannot utilize glucose efficiently, thus an alternative form of energy/fuel is a logical therapeutic approach.