Re: Weird change permit B turned to L ...
While most non-EU permits seem to transfer (assuming employed and a good taxpayer, etc.) I know one person this happened to.
Essentially, permits are issued by the canton; for non EU, changing cantons at least theoretically might mean new rules or conditions.
A further bit of info:
We have C permits, non EU, issued long ago before the various cantonal language requirements came in. Some years ago were were thinking of moving to another canton and were told by Einwohnerkontrolle in the new Gemeinde that an automatic transfer of our existing C permits to the new canton could not be guaranteed, that we would have to meet the new canton's language requirements.
We didn't go any further, so I don't know how that might have played out. We have seen many times that officials make things up as they go along, so who knows if the need to requalify when changing cantons that would have stood up to a challenge.
But it served to underscore the insecurity we feel as non EU citizens.
However, as you can see reading the forum there are plenty of stories of folks who seem to have no trouble getting permits, changing permits, renewing permits even when unemployed.