From what I've seen of the Kenmore a/c remotes, they come in two flavors -- a basic version with just a few buttons on it, and a fancier one that ships with top-of-the-line units and includes an LCD status display (on the remote, that is.)

Which kind do you have? If your Kenmore remote is the kind with an LCD display on it, odds are it uses some sort of two-way protocol and may be difficult if not impossible to emulate in a regular universal remote.

On the other hand, if you have the basic Kenmore remote, its codes can probably be learned. If you haven't yet purchased a universal remote, be sure to get one that supports learning. That may be all you need (and if it works, you can then share with others through the JP1 route).