Which cells in our immune system allow vaccines to work?

In your small intestine is where it's absorbed these cells are usally Cuboidal cells that are good in absorption

Lymphocytes enable the body to remember antigens and to distinguish self from harmful non self (including viruses and bacteria) ... The immune system can remember every antigen encountered because after an encounter, some lymphocytes develop into memory cells. These cells live a long time-for years or even decades.