How do I become a permanent resident after a successful asylum claim in Canada?

Being accepted as a refugee does not by itself make you a permanent resident. After the IRB decides you are a Convention refugee or person in need of protection, you become a protected person.

As a protected person you can then apply for permanent residence from within Canada, using the application designed for Protected Persons and Convention Refugees. Processing fees apply for you and for each family member included, and you can list eligible dependants, including those abroad, in that application.