Smokers with Alzheimer's are a real challenge because, with advancing age, they're already at a point when there are a lot of things they can no longer do. A caregiver always needs to be aware of that. The goal is to help your mother maintain as much of her independence as possible. Still, that has its limits.
When someone has Alzheimer's or another type of dementia, the top priorities become safety and health. You don't want your mom to set the house on fire. (Likewise, you don't want her to develop cancer, although a lifelong smoking habit has, of course, already contributed to that possibility.)
What you can do is take the cigarettes away when you're not with your mother. I'd let her smoke at other times, but only when someone else is with her. Don't make cigarettes available otherwise. And if she can't drive, she can't buy another pack easily -- or maybe at all.
I'd also look into information about smoking cessation, even at her age. A nicotine patch is often successful. If your mom has early dementia, she might benefit from a cessation program through a local hospital. With advanced dementia, it's hard for her to understand why smoking is a health issue or why she should stop. For elderly longtime smokers, the risk of cancer will already be there regardless of whether they quit; you have to consider whether smoking is a quality-of-life habit for them. Some dementia patients even forget that they ever smoked.