Next year I will move to another Canton (from Zug to Schwyz).
I found one thread here on forum from last year but the website mentioned there (eUmzuhCH) has some problems... and still don't know is it enough.
Can someone advise what authorities I should inform and how ? Should I go to Migration Office in new Kanton or only to commune ? Should I inform also current commune that I want to deregister myself ?
If you are a non-EU national you will need permission to move, because non-EU's permits are typically for working and living in the same canton . It is not guaranteed that a new canton's Migration Office would issue you with a permit. Therefore, you should not de-register from your current commune/municipality until you have first obtained such permission.
Is this a new law? Up to and including November 2022 a non-EU/EFTA person only needed the permission from the canton they move to, but not from the canton they move from. ( Art. 37 FNIA )
Can you please link to this new regulation and where it was announced.
Even if things move solely in Switzerland the Swiss foreigner and immigration law is one of the laws which has seen many reforms and changes. For example it was completely rewritten 2005 and has seen a major overhaul in 2019 and many other changes in between. https://www.fedlex.admin.ch/eli/cc/2007/758/fr/changes
Using 1988 information is misleading and confusing, specially when wrong. At least check the current law if a regulation still applies (the law has been linked in the previous post)