Howto write modules to storage?

You can upload them using the normal Storage button in the middle of the IDE screen and uploading the file from eg https://www.espruino.com/modules/MQTT.min.js to a file called MQTT

I don't think the IDE is smart enough to know that the modules are actually installed on the device and to not re-upload them, but nothing stops you from renaming it MyMQTT on the device, and then doing require("MyMQTT");