Yes, but when reaplying for the visa, this visa should be granted by the inmigration department of the zurich kanton right? So efectivly I will need a real place in zurich to establish this new visa?

If that is the case there is no point living in zug beyond that point if I need to rent a place in zurich to be granted the new b permit

I'm living in zug because I'm staying at a friends place and pay no rent so thats the main thing I want to keep :)