If you apply for New Brunswick, you should intend to settle there and wait until after getting PR to eventually move to another province. If you are interested in another province, I would suggest to apply there directly.
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What are the restrictions on employment with Canadian investment immigration?
I want to immigrate to Canada through the New Brunswick program. Am I allowed to work and travel in other provinces if I obtain residency there? Are there any restrictions?
You must intend to live on NB.