PKS 1830-211 is a γ-ray emitting, high-redshift (z =2.507 ± 0.002), lensed flat-spectrum radio quasar. During the period 2019 mid-February to mid-April, this source underwent a series of strong γ-ray flares that were detected by both AGILE-GRID (Gamma-Ray Imaging Detector) and Fermi Large Area Telescope (Fermi-LAT), reaching a maximum γ-ray flux of F_{E>100 MeV} ≈2.3 ×10⁻⁵ photons cm⁻² s⁻¹. Here, we report on a coordinated campaign from both on-ground [Medicina, Owens Valley Radio Observatory (OVRO), Rapid Eye Mount (REM), and Sardinia Radio Telescope (SRT)] and orbiting facilities (AGILE, Fermi, INTEGRAL, NuSTAR, Swift, and Chandra), with the aim of investigating the multiwavelength properties of PKS 1830-211 through nearly simultaneous observations presented here for the first time. We find a possible break in the radio spectra in different epochs above 15 GHz, and a clear maximum of the 15 GHz data approximately 110 d after the γ-ray main activity periods. The spectral energy distribution shows a very pronounced Compton dominance (> 200) which challenges the canonical one-component emission model. Therefore, we propose that the cooled electrons of the first component are re-accelerated to a second component by, for example, kink or tearing instability during the γ-ray flaring periods. We also note that PKS 1830-211 could be a promising candidate for future observations with both Compton satellites [e.g. enhanced ASTROGAM (e-ASTROGAM)] and Cherenkov arrays [Cherenkov Telescope Array Observatory (CTAO)] which will help, thanks to their improved sensitivity, in extending the data availability in energy bands currently uncovered.