A clear picture of charge transport properties in salt-in-ionic liquid electrolyte (SILE) is indispensable for the applications in lithium-ion batteries. In this study, we applied molecular dynamics (MD) simulations on a typical SILE system, composed of lithium bis(fluorosulfonyl)imide (LiFSI) with a molar fraction of 0.3 doped in 1-ethyl-3-methylimidazolium bis(fluorosulfonyl)imide (EMIMFSI). Based on the MD simulations, we calculated conductivity spectra from 108 Hz to 1014 Hz, charge current correlation functions, and charge mean square displacements, based on the center-of-mass (COM) velocities of the ions. The conductivity spectra show a bimodal feature between 1012 Hz and 1013 Hz, attributed to the interionic vibrations of the EMIM+-FSI- and Li+-FSI- contact ion pairs, respectively. Structural relaxation is observed between 109 Hz and 1012 Hz, and a flat plateau below 109 Hz, attributed to the direct current (DC) conductivity. For this SILE composed of three constituent ions, i.e., Li+, EMIM+, and FSI-, the above transport properties are further partitioned to the contributions of the individual constituent ions, including self, distinct contribution of the same constituent ions, and also the cross correlation between them. Detailed analyses on the individual contributions reveal strongly correlated motions in this complex ionic system.