Proton-${}^3$H elastic scattering and charge-exchange reaction ${}^3$H$(p,n){}^3$He in the energy regime above four-nucleon breakup threshold are described in the momentum-space transition operator framework. Fully converged results are obtained using realistic two-nucleon potentials and two-proton Coulomb force as dynamic input. Differential cross section, proton analyzing power, outgoing neutron polarization, and proton-to-neutron polarization transfer coefficients are calculated between 6 and 30 MeV proton beam energy. Good agreement with the experimental data is found for the differential cross section both in elastic and charge-exchange reactions; the latter shows a complicated energy and angular dependence. The most sizable discrepancies between predictions and data are found for the proton analyzing power and outgoing neutron polarization in the charge-exchange reaction, while the respective proton-to-neutron polarization transfer coefficients are well described by the calculations.
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