I tested the li-ion cell how much capacity goes in after charging it with the built in adafruit step up board. I desoldered the cell an put it into my li-ion charger with capacity measurement. The external charger put only 26mAh into the cell before showing FULL. That is only 1% of the measured capacity of the cell. That is OK for me.
I also measuered the time how long the cam is runing after the cell was fully charged. It runs nearly an hour until the red LED begans to flash. That means the voltage of the cell drops below 3,5V, that is the range where the step-up board dont hold the necessary voltage level for the raspberry.
I also know why i had problems with the capacity: if you unplug the charger and the cell is not full and you replug the charger after some seconds, the board shows the cell is full. But it is not. You have to switch off (= separate cell from the loading circuit) and then switch on again. Then loading continues.