  It has been shown that for nonlinear atomic ionization, transfer of the
degree of circular polarization from incident to fluorescence light is maximum
at the Cooper minimum (see Phys. Rev. A \textbf{100}, 011401(R) (2019)). Until
the present, however, it is still a challenge to produce and detect
circularly-polarized light at xuv and x-ray photon energies. We here show, that
transfer of linear polarization is strongly enhanced at the Cooper minimum in
two-photon ionization and can be readily detected using current free-electron
laser facilities by measurements of the degree of linear polarization of the
characteristic $L\alpha_1$ and $L\alpha_2$ lines. Two-photon ionization of
$2p_{3/2}$ electron of tungsten atom is proposed to demonstrate the presented
phenomena and realization of such experiment is discussed in detail.
