The O9.7 V star HD 54879 is currently the only massive magnetic star whose magnetic field geometry and rotation period are not constrained. Over the last 3 yr, we gathered additional observations of this star, obtained using various instruments at several astronomical facilities, with the aim to constrain the rotation period and the magnetic field geometry. The new data include the first full Stokes vector observations with the Potsdam Echelle Polarimetric and Spectroscopic Instrument (PEPSI), installed at the Large Binocular Telescope. The acquired spectropolarimetric observations show a very slow magnetic field variability related to the extremely slow rotation of HD 54879, which is also indicated in a dynamical spectrum, displaying variability of the H alpha line. The most intriguing result of our study is the discovery of differences in longitudinal magnetic field strengths measured using different least-squares deconvolution (LSD) masks containing lines belonging to different elements. It is the first time that such a differential analysis of the field strength in dependence of the used lines is carried out for a magnetic O-type star. Since the LSD Stokes I profiles of the studied O, Si, and He line masks remain stable over all observing epochs, we conclude that the detection of different field strengths using lines belonging to these elements is related to the different formation depths, with the He lines formed much higher in the stellar atmosphere compared to the silicon and the oxygen lines, and non-local thermodynamic equilibrium (NLTE) effects. Our numerical magnetospherical model suggests the presence of enhanced gas density that fills the volume inside the field lines close to the star.