Stem cells won't be a full cure for Alzheimer's
Unlike other cell types in the body, most of our brain cells have very specific connections to other brain cells that form our thoughts and memories. If a brain cell dies from Alzheimer's, replacing that cell won't replace the connections it had with other cells.
If we were suddenly able to replace the brain cells in somebody with a lot of damage from Alzheimer's, that person still won't regain all the memories that were lost, or even the personality. The sad truth is that the person would still be a stranger to you, and vice-versa. Full "recovery" might even mean going back to school for years to relearn lost skills. Even if the Alzheimer's were caught early and we could do a continual replacement of brain cells, it's not clear that the person still wouldn't lose important memories over time.
Ultimately, the only solution for Alzheimer's is to find the cause of the disease and prevent it.