A discrepancy has emerged between the cosmic lithium abundance inferred by the WMAP satellite measurement coupled with the prediction of the standard big-bang nucleosynthesis theory, and the constant Li abundance measured in metal-poor halo dwarf stars (the so-called Spite plateau). Several models are being proposed to explain this discrepancy, involving either new physics, in situ depletion, or the efficient depletion of Li in the pristine Galaxy by a generation of massive first stars. The realm of possibilities may be narrowed considerably by observing stellar populations in different galaxies, which have experienced different evolutionary histories. The WCen stellar system is commonly considered as the remnant of a dwarf galaxy accreted by the Milky Way (MW). We investigate the Li content of a conspicuous sample of unevolved stars in this object. We obtained moderate resolution (R=17000) spectra for 91 main-sequence/early sub-giant branch (MS/SGB) WCen stars using the FLAMES-GIRAFFE/VLT spectrograph. Li abundances were derived by matching the equivalent width of the LiI resonance doublet at 6708A, to the prediction of synthetic spectra computed with different Li abundances. Synthetic spectra were computed using the SYNTHE code along with ATLAS9 model atmospheres. The stars effective temperatures are derived by fitting the wings of the Ha line with synthetic profiles. We obtain a mean content of A(Li)=2.19+-0.14~dex for WCen MS/SGB stars. This is comparable to what is observed in Galactic halo field stars of similar metallicities and temperatures. The Spite plateau seems to be an ubiquitous feature of old, warm metal-poor stars. It exists also in external galaxies, if we accept the current view about the origin of WCen. This implies that the mechanism(s) that causes the cosmological lithium problem may be the same in the MW and other galaxies.