According to the article Roohparvar says the sleeve will also work with 1.2 volt rechargeable batteries, boosting them up to 1.5 volts., but they don't say anything about how well the rechargables would handle this usage.
The usual way for rechargables, I imagine. They'll handle it just fine until they die from an overly deep discharge.
If the chip is very clever, then it'll detect that it's working on a rechargable (from voltage curves?), and stop discharging after a certain point. But the specifics there depend on the exact chemistry used, so it'd be difficult to get it right.
