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We present a multi-wavelength analysis of two highly magnified strong gravitationally lensed galaxies, CLASS B0712+472 and CLASS B1608+656, at redshifts $1.34$ and $1.394$, respectively, using new VLBI and archival HST observations. We reconstruct the positions of the radio and optical emissions with their uncertainties using Monte Carlo sampling. We find that in CLASS B0712+472 the optical and radio emissions are co-spatial within $2\pm5$ mas ($17\pm 42$ pc at redshift of 1.34). But, in CLASS B1608+656, we reconstruct an optical-radio offset of $25\pm16$ mas ($214\pm137$ pc at redshift of 1.394), the smallest offset measured for an AGN at such high redshift. The spectral features indicate that CLASS B1608+656 is a post-merger galaxy, which, in combination with the optical-VLBI offset reported here, makes CLASS B1608+656 a promising candidate for a high-$z$ offset-AGN. Furthermore, the milliarcsecond angular resolution of the VLBI observations combined with the precise lens models allow us to spatially locate the radio emission at $0.05$ mas precision ($0.4$ pc) in CLASS B0712+472, and $0.009$ mas precision ($0.08$ pc) in CLASS B1608+656. The search for optical-radio offsets in high redshift galaxies will be eased by the upcoming synoptic all-sky surveys, including E-ELT and SKA, which are expected to find $\sim 10^5$ strongly lensed galaxies, opening an era of large strong lensing samples observed at high angular resolution.