A team involved in the Apache Point Observatory Galactic Evolution Experiment (APOGEE), one of the Sloan Digital Sky Survey III programmes, recently announced the discovery of two rare rigidly rotating magnetosphere stars, HD 345439 and HD 23478. Near-infrared spectra of these objects revealed emission-line behaviour identical to that previously discovered in the helium-strong star sigma Ori E, which has a strong magnetic field and rotates fast. A single spectropolarimetric observation of HD 345439 with the FOcal Reducer low dispersion Spectrograph (FORS 2) at the Very Large Telescope (VLT) in 2014 over 88 min indicated that HD 345439 may host a strong, rapidly varying magnetic field. In this work, we present the results of our spectropolarimetric monitoring of this star with FORS 2, which revealed the presence of a strong longitudinal magnetic field dominated by a dipolar component. The analysis of spectral variability indicates an opposite behaviour of He and Si lines, which is usually attributed to differences in the distribution of surface He and Si abundance spots.