The thermal conductivity is calculated with the Helfand-moment method in the Lennard-Jones fluid near the triple point. The Helfand moment of thermal conductivity is here derived for molecular dynamics with periodic boundary conditions. Thermal conductivity is given by a generalized Einstein relation with this Helfand moment. The authors compute thermal conductivity by this new method and compare it with their own values obtained by the standard Green-Kubo method. The agreement is excellent. (C) 2007 American Institute of Physics.