The false statement is: T lymphocytes produce antibody molecules
B lymphocytes produce antibody molecules.
B cells and T cells or lymphocytes are both cells of the adaptive immune system. Progenitor T cells mature (start to express T cell receptors TCRs, CD4 /CD8 receptors) into T cells in lymphoid organ-thymus. T cell can recognize only those antigens that are presented on antigen-presenting cells, on their surface MHC molecules.
There are three types of T cells: Helper T cells,Cytotoxic T cellsand T regulatory cells.