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Context. Standing and moving shocks in relativistic astrophysical jets are very promising sites for particle acceleration to large Lorentz factors and for the emission from the radio up to the γ -ray band. They are thought to be responsible for at least part of the observed variability in radio-loud active galactic nuclei. Aims. We aim to simulate the interactions of moving shock waves with standing recollimation shocks in structured and magnetized relativistic jets and to characterize the profiles of connected flares in the radio light curve. Methods. Using the relativistic magneto-hydrodynamic code MPI-AMRVAC and a radiative transfer code in post-processing, we explore the influence of the magnetic-field configuration and transverse stratification of an over-pressured jet on its morphology, on the moving shock dynamics, and on the emitted radio light curve. First, we investigate different large-scale magnetic fields with their effects on the standing shocks and on the stratified jet morphology. Secondly, we study the interaction of a moving shock wave with the standing shocks. We calculated the synthetic synchrotron maps and radio light curves and analyze the variability at two frequencies 1 and 15.3 GHz and for several observation angles. Finally, we compare the characteristics of our simulated light curves with radio flares observed from the blazar 3C 273 with the Owens Valley Radio Observatory and Very Long Baseline Array in the MOJAVE survey between 2008 and 2019. Results. We find that in a structured over-pressured relativistic jet, the presence of the large-scale magnetic field structure changes the properties of the standing shock waves and leads to an opening in the jet. The interaction between waves from inner and outer jet components can produce strong standing shocks. When crossing such standing shocks, moving shock waves accompanying overdensities injected in the base of the jet cause very luminous radio flares. The observation of the temporal structure of these flares under different viewing angles probes the jet at different optical depths. At 1 GHz and for small angles, the self-absorption caused by the moving shock wave becomes more important and leads to a drop in the observed flux after it interacts with the brightest standing knot. A weak asymmetry is seen in the shape of the simulated flares, resulting from the remnant emission of the shocked standing shocks. The characteristics of the simulated flares and the correlation of peaks in the light curve with the crossing of moving and standing shocks favor this scenario as an explanation of the observed radio flares of 3C 273.