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Accurate characterization of in utero human brain maturation is critical as it involves complex interconnected structural and functional processes that may influence health later in life. Magnetic resonance imaging is a powerful tool complementary to the ultrasound gold standard to monitor the development of the fetus, especially in the case of equivocal neurological patterns. However, the number of acquisitions of satisfactory quality available in this cohort of sensitive subjects remains scarce, thus hindering the validation of advanced image processing techniques. Numerical simulations can mitigate these limitations by providing a controlled environment with a known ground truth. In this work, we present a flexible numerical framework for clinical T2-weighted Half-Fourier Acquisition Single-shot Turbo spin Echo of the fetal brain. The realistic setup, including stochastic motion of the fetus as well as intensity non-uniformities, provides images of the fetal brain throughout development that are comparable to real data acquired in clinical routine. A case study on super-resolution reconstruction of the fetal brain from synthetic motion-corrupted 2D low-resolution series further demonstrates the potential of such a simulator to optimize post-processing methods for fetal brain magnetic resonance imaging.