Dependence of angular momentum of fission fragments on total kinetic energy in spontaneous fission of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mi>Cf</mml:mi> <mml:mprescripts/> <mml:none/> <mml:mn>252</mml:mn

A weak dependence of the angular momentum of $^{144}\mathrm{Ba}$ fragments, produced in the spontaneous fission of $^{252}\mathrm{Cf}$, on the total kinetic energy (TKE) was recently observed [N. P. Giha et al., Phys. Rev. C 111, 014605 (2025)]. To investigate this phenomenon, we propose a model describing the evolution of the fissioning nucleus toward scission. The model assumes that, after tunneling through the fission barrier, the nucleus can be represented by a superposition of dinuclear systems (DNSs). We calculate main fission observables, including mass, TKE, and neutron multiplicity distributions, and compare them with experimental data. The angular motion in the DNS is treated quantum-mechanically, yielding the angular momentum distribution of DNS nuclei at scission configurations leading to $^{144}\mathrm{Ba}$ fragments. Within this framework, we successfully reproduce and explain the experimentally observed dependence of the average angular momentum of $^{144}\mathrm{Ba}$ on TKE.