That would have a Lead Acid battery, the charge would only go to 13.6VDC (if thecharger were left plugged in to AC power).
Usually these die because the battery is allowed to fully discharge (just before you needed it).
So the simple answer is, it is not economically feasible to directly recreate this device.
That being said, if one were to integrate the RYOBI charger in place of the existing charging circuit and patch the battery circuit to the chargers +&- terminals of the batteries circuit (inside the charger) .
You might have a RYOBIish portable power unit with a replicable battery.
You might even add an inverter for 120vAC power.
Go crazy just remember you could end up burning down your house , electrocuting yourself, maybe causing world war III.
just publish your progress so we can all learn what NOT to do.