Recent neutron-scattering experiments on La(2-x)Sr(x)CuO4 single crystals by Wakimoto et al. have revealed that elastic magnetic peaks appear at low temperatures in both insulating (x=0.02-0.05) and superconducting (x=0.06) samples. We have carried out further investigations particularly on the elastic incommensurate peaks for x=0.06, and found that the integrated intensity drastically changes across the low temperature insulator- superconductor boundary; the intensity of x=0.06 is 4 times smaller than that of x=0.05, while the intensity in the insulating region stays constant.