I have tried quite a lot of things, but the M003 modules did not find any satellites. At least the PPS pulses should be present even without any core connected if the modules are powered with 3.3V. Probably I received two defect devices.
Meanwhile I bought two GPS units of type AT6558. They are less expensive and they do now their job without any problem. They have even the advantage of an integrated voltage regulator, so they are not dependant of a power supply with an exactly regulated voltage value.
It is just a little bit tricky if one wants to use the pps output of the GPS chip as it is already connected with a blue LED inside the device (not visible if case is closed). So some soldering work has to be done.