Here’s the only method I have found:
You need to record a short MIDI song on the Genos. There needs to be at least one note in every MIDI channel for which you want the mixer settings to be saved. You can make that happen using the step editor.
You can then transfer the song file to your computer and import it into the DAW of your choice. From there you can see the MIDI messages that set the instrument for each channel.
Once you have those MIDI messages, you can insert them into the beginning of any song you are building in your DAW, and the instruments will be set properly in your mixer.
You also might be able to look up the required MIDI messages in the Genos docs (probably the Data List), and then you could just create them directly inside your DAW.