I understand that HIV directly affects the helper t cell population. And that t cells are necessary to stimulate B cells, B cells to differentiate into plasma cells, finally secreting antibodies. Of course as time passes, the virus depletes the t cell population. how come transfusions of t cells cannot take place in order to increase the amount within the body? Wouldn't that solve the problem?

That is a great question. Unfortunately giving t cells to someone with HIV is like giving them an organ transplant. The t cells would be recognized as foreign and would be destroyed. If you could get a good match, you would likely need to also give immunosuppressive drugs to suppress the immune system from killing the foreign t cells.