The Agreement on the Free Movement of Persons has been in force since 1 June 2002 between Switzerland and the European Community as well as its member states. This gives citizens of the European Union (and EFTA) the right to enter and stay in Switzerland, provided they satisfy the requirements provided for in the Agreement.  Read more...  (admin.ch)

Moving within the Canton of Zug / Moving Abroad
If you move within the canton you must officially confirm termination of residence in your previous town at the local Residents’ Registry Office (Einwohnerkontrolle). In this connection foreign residents must present their residence permits.

Moving to another Canton
If you move to another canton you must officially confirm termination of residence in your previous town or municipality at the local Residents’ Registry Office (Einwohnerkontrolle). Non-EU/EFTA nationals planning to move to another canton are advised to first make their application to the responsible authorities in the new canton and only to move there once the residence permit has been issued.