Hi Chamzamzoo, have you come across this, it might do what you want:
The extension battery feeds this regulator which you adjust to give up to 2A at up to the fully charged voltage of the original battery. Then to the original battery it looks like a charger and supplies the first 2A of {charging current + motor load}, if any.
Unlike the 'batteries in parallel' method no mods are needed to the original battery, no diode in other words, which I'd guess is why the bike's makers chose the 'extender' route.
The battery voltages needn't be matched, the extender battery's voltage can safely be higher, or it can be lower and will be boosted as needed (up to a point).
This does rely on the external battery cells having a generous current rating, and on its LVC protection, and on the original BMS working with an extender (tick). You should gain about 80% of the extender pack's capacity.
I'd fit a diode in the regulator's output, just in case, and choosing similar battery voltages should make for a stable, efficient regulator. I've not used this one myself but maybe it's worth a punt.
Anthony