[zitoune]

...solder at least one pin of the module to the PCB, let's say GND

Important: Never solder the GND pin of the TX module to any other GND point than the one marked as GND on the TX module connector.
If you give a look at the schematics you will know why!

Indeed. I meant that instead of using 4 'soft' wires to connect the module to the PCB, use one original PIN (header PIN - any of the 4) to make a "hard" connexion and thus maintain in place the module to the PCB - in my case I chose the GND, but it could be any. The rest (3 pins) would be soldered with 'soft' wires.
[I'll take a pict]

And we know (or not?) why the 2 GND are different

Thanks
Zitoune