Are you coming from an upgrade? If so, you may want to import the default security roles from the demo database.
To answer your question, the security role to post the Purchase invoice is P&P-Q/O/I/R/C, POST. However, as with any release of NAV, you will need to manually add missing tables in the permission and test it out by trial and error.
For the My Vendors table, you will need to add a role for these tables. For some reason, it's left out of the permissions list.
