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We present the first measurements of femtoscopic correlations between the K0S and K± particles in pp collisions at s√=7 TeV measured by the ALICE experiment. The observed femtoscopic correlations are consistent with final-state interactions proceeding solely via the a0(980) resonance. The extracted kaon source radius and correlation strength parameters for K0SK− are found to be equal within the experimental uncertainties to those for K0SK+. Results of the present study are compared with those from identical-kaon femtoscopic studies also performed with pp collisions at s√=7 TeV by ALICE and with a K0SK± measurement in Pb-Pb collisions at sNN−−−√=2.76 TeV. Combined with the Pb-Pb results, our pp analysis is found to be compatible with the interpretation of the a0(980) having a tetraquark structure instead of that of a diquark.