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The longitudinal spin transfer DLL to Λ and Λ hyperons produced in high-energy polarized proton-proton collisions is expected to be sensitive to the helicity distribution functions of strange quarks and antiquarks of the proton, and to longitudinally polarized fragmentation functions. We report an improved measurement of DLL from data obtained at a center-of-mass energy of √s = 200 GeV with the STAR detector at RHIC. The data have an approximately twelve times larger figure of merit than prior results and cover |η| < 1.2 in pseudorapidity with transverse momenta pT up to 6 GeV / c. In the forward scattering hemisphere at largest pT, the longitudinal spin transfer is found to be DLL = −0.036 ± 0.048 (stat) ± 0.013 (sys) for Λ hyperons and DLL = 0.032 ± 0.043 (stat) ± 0.013 ( sys ) for Λ antihyperons. The dependences on η and pT are presented and compared with model evaluations.