The BH Evo 36V charger (above) output lead only has two wires soldered onto the board (+ and -), so I suppose it has no "communication" with the battery. The sticker on the back is incorrect, as there is no NTC-thermistor either (meaning heat sensor). The BMS on the battery merely opens the circuit when it's had enough juice, at around 41,8V in my case.
The thing then to look out for is that the generic charger is meant for a wide range of 42V (36V) e-bikes, and doesn't go too far above the 42V before cutting off even if the BMS fails to cut it.
My original 36V BH charger died, so I ordered an official BH replacement charger from Doctibike (France), and also used the old dead charger's lead to solder a female barrel connector onto it, that came with a generic charger kit that had swappable adapters for various e-bikes. It was from a local big chain store that sells it to use on their e-bikes and others. I've been using the generic at work and the official charger at home for a few months now no problem. The replacement BH charger was 160 eur with shpping, and the generic charger is 55e with shipping.
My local electronics repair shop did the soldering and testing, so it's got proper insulation and strain relief etc.
Generic "GZR 4-in-1" with BH Singatron 3-pin plug (and battery adapter pigtail) soldered onto a barrel connector (just skip the barrel connector and solder straight to the output of the generic charger, as the barrel connector can cause some heat lossess even at ~2A):
View attachment 152818
Official BH replacement from Doctibike:
View attachment 152819
Official BH replacement from Doctibike (the output "36V" is wrong, should be 42V since 36V would only get you to half full battery, but now the NTC is ignored which is correct):
View attachment 152820
BH old official charger output lead connector, only + and - are connected:
View attachment 152824
BH old charger circuit board underside: