  The magnetic response of CaK(Fe$_{0.949}$Ni$_{0.051}$)$_4$As$_4$ was
investigated by means of the muon-spin rotation/relaxation. The long-range
commensurate magnetic order sets in below the N\'{e}el temperature $T_{\rm N}=
50.0(5)$~K. The density-functional theory calculations have identified three
possible muon stopping sites. The experimental data were found to be consistent
with only one type of magnetic structure, namely, the long-range magnetic
spin-vortex-crystal order with the hedgehog motif within the $ab-$plane and the
antiferromagnetic stacking along the $c-$direction. The value of the ordered
magnetic moment at $T\approx3$ K was estimated to be $m_{\rm Fe}=0.38(11)$
$\mu_{\rm B}$ ($\mu_{\rm B}$ is the Bohr magneton). A microscopic coexistence
of magnetic and superconducting phases accompanied by a reduction of the
magnetic order parameter below the superconducting transition temperature
$T_{\rm c}\simeq 9$ K is observed. Comparison with 11, 122, and 1144 families
of Fe-based pnictides points to existence of correlation between the reduction
of the magnetic order parameter at $T\rightarrow 0$ and the ratio of the
transition temperatures $T_{\rm c}/T_{\rm N}$. Such correlations were found to
be described by Machida's model for coexistence of itinerant spin-density wave
magnetism and superconductivity [Machida, J. Phys. Soc. Jpn. 50, 2195 (1981)
and Bud'ko et al., Phys. Rev. B 98, 144520 (2018)].
