Usually and most likely, No.
Here are 2 scenerios that would be Yes:
If a person already has chronic HepB and don't know it, and got vaccinated, then the vaccine won't work. This person could infect others.
If the person is not infected, got vaccinated, and is a non-responder to the vaccine (meaning not developing the protective antibodies needed for immunity), then this person could get infected and infect others.
I am sorry, my question is if a person has been vaccinated against Hep B, can they still carry the virus and give it?
"if they were VACCINATED after having already been infected."
Sorry about that.
Yes, one encounter could. It only takes one.
No symptoms is usually a good sign in an adult recently infected but does not eliminate the possibility of infection. You've been tested twice since the encounter? I wouldn't worry too much.
A person can still be a carrier if they were infected after having already been infected.
Do yourself a favor and learn something from this. Sounds like you dodged a bullet this time but why put yourself through this?