A cheap LiIon 9V battery from China
Overcharge protection on the A cell kicks in at 8,46 volt and over discharge protection at 5,53V
Overcharge protection on the B cell kicks in at 8,46 volt and over discharge protection at 5,56V
It do not have the rated 800mAh, but the discharge curves looks good for a 590mAh battery.
Conclusion
The capacity rating is too high, but it looks like a acceptable LiIon 9V battery.
8.4 volts (when freshly charged), and around 7.5 volts over most of the run time, just won’t cut it for a lot of devices that require 9 volt batteries. I have smoke detectors that start sounding the low battery warning at around 7.6v. I use NiMH 9v batteries in them, but they use 7 internal cells for a total of 9.6v.
This battery would start sounding the warning way too soon. Though, the greater capacity might still give it a decent run-time.
BTW, how do you charge it? It must come with a special charger?
Battery seems equipped with a proper management system. Undervoltage protection is likely set at 2.75V/cell (battery cut offs: 5.53 and 5.56V). Cell balancing may be absent, of course.
It can also be done with a generic CC/CV power supply, just set maximum voltage and current to the desired values. HKJ used 8.4V and 0.2A for the above-mentioned charging graph.