Powering MDBT42Q over battery connected to recharger?

Hi,
I would like to power the MDBT42Q through a battery which is connected to a charger. I tried to connect the charger pins (5V & GND) to to pins of the MDBT42Q (GND, V+), which are used if I would connect to battery directly. Unfortunately the board does not react. Is it possible to power the board over the recharger?

When I connect it to the Bat and GND pin, it seems to work. Is this the right connection? And where does the other pin stands for?

Here are some illustrations of the connections:

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Is it possible to power the board over the recharger?

Depends on the recharger. A good recharger detects the battery voltage and polarity and won't provide any power to a dead battery (0 V) or with wrong polarity (negative). It seems you have a good recharger.

When I connect it to the Bat and GND pin, it seems to work. Is this the right connection?

Yes. There is the risk of overloading your charger if your circuit draws more current than the charger can provide. If you connect only the MDBT42Q it'll be fine, but if you add a motor or 100 neopixels you might eventually overload the charger once the battery is drained.

Yes, that looks fine - as @maze1980 says the charger may well not provide any power without a battery also attached.

Only thing I'd say is there's actually a specific set of 2mm spaced holes for the JST connector (see the pic) - these have the same connections as you used but it allows you to still add pins, or to use the power pins down the side to connect other stuff.

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Do you think that I could solder it also directly to the NRF51822 BLE module instead of the MDBT42Q?
Here is the schematic: https://learn.adafruit.com/assets/17043
Here is the datasheet: https://cdn-shop.adafruit.com/datasheets/MCP73831.pdf

The voltage range would be lower (Wide supply voltage range (1.8V to 3.6V)). Does such a charger have a voltage regulator?

NRF51822? Or you mean the blue/silver module - which is actually an MDBT42Q?

I'm afraid you can't do it directly no. The MDBT42Q breakout board has a voltage regulator that takes the ~4.2v from the lithium battery down to a 3.3v that the chip can manage. You could always add your own though

A charger for LiPo goes up to 4.2V (and more), a charger for LiFePo4 would go up to 3.6V or max. 3.75V which could be acceptable. You'd need a different charger and a LiFePo4 battery, too. And since there's no voltage regulator involved that would fail at at low battery voltage should detect low battery voltage yourself. Otherwise the chip would drain the battery until it's dead and broken.

As far as I remember, the 5V pin is directly connected to the 5V pin of the USB header. That is: you will get 5 V from the charger only you have it connected via USB to a power source.

In order to integrate the charger into your project, you would power the MDBT42Q using the BAT and GND pins of the charger, connect the LiPo battery to the charger and using the USB port of the charger to charge the battery when needed.