We explore the mass content of galaxies residing in galaxy clusters at z=0 in the EAGLE hydrodynamical simulation as well as the galaxies' mass build-up through cosmic time. We use a galaxy catalogue generated with the HBT+ algorithm, which identifies subhaloes consistently over time by tracking their dynamical evolution throughout the simulation. The satellite subhalo-to-stellar mass relation (SHSMR) is well described by a double power-law. At stellar masses $9<\log m_\star/\mathrm{M}_\odot<10$, satellites have 20-25% the subhalo mass of central galaxies at fixed stellar mass. At high stellar masses the satellite SHSMR is consistent with that of centrals. The satellite SHSMR decreases steeply for satellites closer to the cluster centre, even in projection, broadly consistent with recent weak lensing measurements. The scatter in the satellite SHSMR is larger than that of central galaxies at all cluster masses and cluster-centric distances $RComment: 19 pages, 16 figures including 2 short appendices.Accepted for publication in A&A. Code is available at https://github.com/cristobal-sifon/eagle-satellites