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We report on domain pattern transfer from a ferroelectric BaTiO3 substrate to a CoFeB wedge film with a thickness of up to 150 nm. Strain coupling to domains in BaTiO3 induces a regular modulation of uniaxial magnetic anisotropy in CoFeB via an inverse magnetostriction effect. As a result, the domain structures of the CoFeB wedge film and BaTiO3 substrate correlate fully and straight ferroelectric domain boundaries in BaTiO3 pin magnetic domain walls in CoFeB. We use X-ray photoemission electron microscopy and magneto-optical Kerr effect microscopy to characterize the spin structure of the pinned domain walls. In a rotating magnetic field, abrupt and reversible transitions between two domain wall types occur, namely, narrow walls where the magnetization vectors align head-to-tail and much broader walls with alternating head-to-head and tail-to-tail magnetization configurations. We characterize variations of the domain wall spin structure as a function of magnetic field strength and CoFeB film thickness and compare the experimental results with micromagnetic simulations.