Did you apply for initial licensure in CA? If so, there is no reason for you to send anything to them, as far as passing the NCLEX exam. They get the results directly from Pearosn-Vue.
Once you submit the SSN# to them, it is just a matter of a week or so before you will have your license sent to you and see your name on the CA BRN webite. (CA does not have a BON, they have a BRN-Board of Registered Nursing/ LVNs are handled by a completely separate dept.)