It sounds like sedum 'Autumn Joy' and yes, you can divide it. In fact, they tend to spread very much, so you'll have lots of plants to give away. I wouldn't divide them until the spring, though, because they're blooming now. The flowers start out pink and then darken to a bronze color.

You could send her a division in the spring. Depending on how much the postage costs, she may be better off just buying one locally. They're a common perennial.

Sedum is the name of the plant, there are hundreds of varieties.

They can be divided in the fall or spring, however an easy way to propagate is by stem cuttings which can be cut in the spring and rooted. If it is the kind that forms rosettes in the spring, you could break one off and mail to your mother.

Here is a link that might be useful: About Sedum