[engolling]

Could you power up the system on the input with no load on the output attached and make the 6 voltage measurements described in the picture.
I also see that there are also some other XL6009 with display than the one I use

I do not see the measurement point N ° 4 

1 B+B-  > 8.35V
2 Vin-Vin+ > 8.35V
3 Vout-Vout+ > 12.06
4??
5 B+Bm > 4.21V
6 BmB- > 4.13

The 4th point was to check if you are reading carefully   ... no I just messed it up because I can not count until 4 .

All of the values are fine.

If I understood you right - everything works but if you are on battery it stops within one hour and switches off unti you supply it again.
Could you let it run on battery and do the 5 measurements about each 15minutes.
Maybe one of the cells is bad.

Regards,
Stefan