The Cosmic Ray Telescope for the Effects of Radiation (CRaTER), an instrument carried on the Lunar Reconnaissance Orbiter spacecraft, directly measures the energy depositions by solar and galactic cosmic radiations in its silicon wafer detectors. These energy depositions are converted to linear energy transfer (LET) spectra. High LET particles, which are mainly high-energy heavy ions found in the incident cosmic ray spectrum, or target fragments and recoils produced by protons and heavier ions, are of particular importance because of their potential to cause significant damage to human tissue and electronic components. Aside from providing LET data useful for space radiation risk analyses for lunar missions, the observed LET spectra can also be used to help validate space radiation transport codes, used for shielding design and risk assessment applications, which is a major thrust of this work. In this work the Monte Carlo transport code HETC-HEDS (High-Energy Transport Code-Human Exploration and Development in Space) is used to estimate LET contributions from the incident primary ions and their charged secondaries produced by nuclear collisions as they pass through the three pairs of silicon detectors. Also in this work, the contributions to the LET of the primary ions and their charged secondaries are analyzed and compared with estimates obtained using the deterministic space radiation code HZETRN 2010, developed at NASA Langley Research Center. LET estimates obtained from the two transport codes are compared with measurements of LET from the CRaTER instrument during the mission. Overall, a comparison of the LET predictions of the HETC-HEDS code to the predictions of the HZETRN code displays good agreement. The code predictions are also in good agreement with the CRaTER LET measurements above 15 keV/µm but differ from the measurements for smaller values of LET. A possible reason for this disagreement between measured and calculated spectra below 15 keV/µm is an inadequate representation of the light ion spectra in HETC-HEDS and HZETRN code calculations. It is also clear from the results of this work that Vavilov distributions need to be incorporated into the HETC-HJEDS code before it will be able to recreate the observed LET spectra measured by the CRaTER instrument.