When you become Permanent Resident (PR) through one of the Provincial Nominee Programs (PNP), moving out of the province that nominated you is a little trickier. Indeed, when you apply to receive a provincial nomination, you sign a letter indicating your intent to settle in the province, and in some cases like in New Brunswick, you even sign a commitment to reside in the province.
The fact of the matter is, one of the main reasons why provinces grant a nomination is for you to reside in the province and contribute to its economic development. It often happens that a province withdraws its provincial nomination before the PR status is granted. This will happen if someone lives in a province (working or studying), applies and receives a provincial nomination, and then moves out of the province before the PR application is processed and PR status granted.
As soon as you get the PR status, you are protected by the Canadian Charter of Rights and Freedoms and its Article 6 ("Mobility Rights" ). Some might think that these rights guarantee free movement between provinces, however, there are some limitations to these rights, and one of the most important is the Provincial Nominee Programs (PNP). But nowhere in the law is there a minimum stay period in the nominating province. The law on this point remains ambiguous and open to interpretation.
This is why you need to be careful when deciding to move out a province that nominated you after getting PR status. This province can come after you, requesting IRCC to revoke your PR status on the grounds of misrepresentation. Indeed, the province will say that you misrepresented your intent to stay in the province and had no intention in residing and living in the province. If this request goes through and you are found to have misrepresented your intent, you will be deported and be inadmissible to enter Canada for 5 years.
However, you can defend yourself in these situations (see below what you can do to prove intent) and it is also not automatic that you will be pursued for misrepresentation if you decide to leave the province that nominated you. Usually, this will happen very often if you don't even bother to try and settle in the province. New Brunswick, for example, requires its nominees to register in person in the province within 30 days of landing in Canada, and will try to revoke PR status for those who haven't done so (after several follow-ups).