Ok, the external battery has a capacity of 150mAh instead 800mAh. I have connected the trackers now to the right high capacity batteries. This is a temporary solution for us. Later they will be connected to a 12V power supply.
I have noticed that when the FMB920 has no efficient power supply connected, it is shutting down, also when there is sufficient internal battery capacity. that is weird. For example it is shutting down while current internal battery is 60%.
Btw, the internal battery is charging till 80% when connected to a 9V 800mAh li-on battery.
The devices are active for about 3 hours a day. For the rest of the day they are in Deep Sleep mode.