Thank you. that helps alot!
If your Hep B Core anti-body is negative, this means you have never been infected with HBV.
I have to assume that when you say "Hep B virus surface", you mean Hep B surface anti-body (HBsAb) and NOT surface antigen (HBsAg). If your surface anti-body titer results are positive, this should mean that you are immune. Usually you want to see a titer of >10 IU/ML to confirm immunity.
Once you have confirmation of immunity, you should remain immune for life even though the titer results may drop over time.