In the gravitational lens SDSS J1004+4112, a background quasar is lensed by a galaxy cluster, hence the light from the quasar images travels mainly through the intracluster medium. Observations in the continuum emission and the broad line region detected variability due to microlensing in the multiple images of the quasar. In this work, we use the 14.5-year monitoring campaign in r-band and the time delays derived from these light curves by Muñoz et al. (2022), to study their microlensing signature. We compare the observed microlensing differences between image pairs with Bayesian models to determine the stellar mass fractions at the image positions in the galaxy cluster and the quasar accretion disk size. We find a quasar half-light radius of 6.4+0.7-0.3 √{M/0.3M⊙} light-days at 2407Å in the rest frame, compatible with previous estimates. The stellar mass fractions at the four positions of the quasar images are αA=0.080+0.104-0.018, αB=0.056+0.066-0.032, αC=0.021+0.039-0.021 and αD=0.072+0.063-0.036. These estimates are compatible within 1σ with the expected fraction determined through intracluster light studies except for the first value, which is around 3σ discrepant. This may indicate the presence of an undetected stellar component in this region. Thus, quasar microlensing provides an independent probe of the intracluster medium and the extension to other lensing galaxy clusters will allow us to determine whether the inferences are compatible with direct observations of the intracluster light.