I recently moved from Zug to Geneva and my company's payroll people handled the process. I had to complete a form for the Geneva authority, which is the same form that a newcomer to Switzerland would complete, and that was sent off with 2 passport photos. My existing permit is to be sent back to Zug authority (which I will do when I eventually receive my permit from Geneva). I am still waiting for my Geneva permit after over a month.....

I had previously moved within Zug canton and only had to send off my B permit with a letter giving them my new address - much easier!