  We study the inclusive photoproduction of $T_{{\bar c}{\bar c}}(3875)^-$
mesons (which are the antiparticles of the doubly charmed tetraquarks
$T_{cc}(3875)^+$ discovered recently by the LHCb Collaboration) from nuclei in
the near-threshold energy region within the nuclear spectral function approach
by considering incoherent direct (${\gamma}p(n) \to D^+(D^0){T_{{\bar c}{\bar
c}}(3875)^-}\Lambda^+_c$) photon--nucleon $T_{{\bar c}{\bar c}}(3875)^-$
creation processes as well as five possible different scenarios for their
internal structure with the main goal of clarifying the possibility to decipher
this structure (and, hence, that of $T_{cc}(3875)^+$) in photoproduction via
integral and differential observables. We calculate the absolute and relative
excitation functions for $T_{{\bar c}{\bar c}}(3875)^-$ production off $^{12}$C
and $^{184}$W target nuclei at near-threshold photon beam energies of 30--38
GeV, the absolute differential cross sections for their production off these
target nuclei at laboratory polar angles of 0$^{\circ}$--10$^{\circ}$ as well
as the A and momentum dependences of the relative (transparency ratios) cross
sections for $T_{{\bar c}{\bar c}}(3875)^-$ production at photon energy of 35
GeV within the adopted scenarios for the $T_{{\bar c}{\bar c}}(3875)^-$ meson
intrinsic structure. We demonstrate that the absolute and relative observables
considered show a certain sensitivity to these scenarios. Therefore, the
measurement of such observables in future experiments at the proposed
high-luminosity electron-ion colliders EIC and EicC in the US and China in the
near-threshold energy region might shed light on the $T_{cc}(3875)^+$ internal
structure.
