Data from the Euclid space telescope will enable cosmic shear measurements to be carried out with very small statistical errors, necessitating a corresponding level of systematic error control. A common approach to correct for shear biases involves calibrating shape measurement methods using image simulations with known input shear. Given their high resolution, galaxies observed with the Hubble Space Telescope (HST) can, in principle, be utilised to emulate Euclid observations of sheared galaxy images with realistic morphologies. In this work, we employ a GalSim-based testing environment to investigate whether uncertainties in the HST point spread function (PSF) model or in data processing techniques introduce significant biases in weak-lensing (WL) shear calibration. We used single Sérsic galaxy models to simulate both HST and Euclid observations. We then 'Euclidised' our HST simulations and compared the results with the directly simulated Euclid-like images. For this comparison, we utilised a moment-based shape measurement algorithm and galaxy model fits. Through the Euclidisation procedure, we e_ectively reduced the residual multiplicative biases in shear measurements to sub-percent levels. This achievement was made possible by employing either the native pixel scales of the instruments, utilising the Lanczos15 interpolation kernel, correcting for noise correlations, and ensuring consistent galaxy signal-to-noise ratios between simulation branches. Alternatively, a finer pixel scale can be employed alongside deeper HST data. However, the Euclidisation procedure requires further analysis on the impact of the correlated noise, to estimate calibration bias. We found that additive biases can be mitigated by applying a post-deconvolution isotropisation in the Euclidisation set-up. Additionally, we conducted an in-depth analysis of the accuracy of TinyTim HST PSF models using star fields observed in the F606W and F814W filters. We observe that F606W images exhibit a broader scatter in the recovered best-fit focus, compared to those in the F814W filter. Estimating the focus value for the F606W filter in lower stellar density regimes has allowed us to reveal significant statistical uncertainties.