We report the results of a theoretical investigation of the electronic structure of the ${\mathrm{ThF}}^{+}$ cation, which is one of the most interesting systems to search for the electron electric dipole moment $(e\mathrm{EDM})$ [H. Loh, K. C. Cossel, M. C. Grau, K.-K. Ni, E. R. Meyer, J. L. Bohn, J. Ye, and E. A. Cornell, Science 342, 1220 (2013)] and other effects of violation of time reversal (T) and spatial parity (P) symmetries in fundamental interactions. For the working ${}^{3}{\ensuremath{\Delta}}_{1}$ state we find a quite high value of the effective electric field acting on unpaired electrons (37.3 GV/cm). The field will be required to interpret the experiment planned on ${\mathrm{ThF}}^{+}$ in terms of the $e\mathrm{EDM}$. Within the concept of atoms in compounds [A. V. Titov, Y. V. Lomachuk, and L. V. Skripnikov, Phys. Rev. A 90, 052522 (2014)], we compare the ${\mathrm{ThF}}^{+}$ electronic structure with that of ThO. Also, we calculate other parameters of T,P-odd interactions: ${W}_{T,P}$, which is needed for interpretation of the experiment in terms of the dimensionless constant ${k}_{T,P}$ characterizing the strength of the $T,P$-odd pseudoscalar-scalar electron-nucleus neutral current interaction (50 kHz); and ${W}_{M}$, which is required to search for the $^{229}\mathrm{Th}$ nuclear magnetic quadrupole moment in ${}^{229}{\mathrm{ThF}}^{+}$ (0.88 $\frac{{10}^{33}\phantom{\rule{0.28em}{0ex}}\mathrm{Hz}}{e\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{2}})$. A number of properties which can be measured are also calculated: the hyperfine structure constant, molecule-frame dipole moment, and $g$ factor.