Here is a chart from here how to read the Hepatitis B blood test result:
According to this chart, if someone gets “negative HBsAg” and “positive HBsAb”, he is immune without any further action. Otherwise he may need either vaccine or more testing.
Here is an example(from here):
The result is “positive HBsAg / negative HBsAb / positive HBcAb”, aka “+ - +”, which means infected according to the chart above.