We report computational simulation results addressing the ionization response of liquid water upon valence ionization. The simulations cover ionizations in the whole valence-orbital range of liquid water, i.e., vacancies in 1b1, 3a1, 1b2, and 2a1 orbitals. It is found that ionization in any of these valence orbitals leads to rapid proton-transfer dynamics. The timescale on which the proton transfer occurs depends on which type of orbital is ionized. For ionization in the 2a1 orbitals, the proton transfer takes place in about 22 fs, competing with the intermolecular Coulombic decay mechanism that takes place on a similar timescale. This result is discussed in the context of earlier experimental results (Richter et al., Nat. Commun. 9, 4988) regarding the intermolecular Coulombic decay in water. For ionization in the outer-valence orbitals (1b1, 3a1, 1b2), we see rapid internal conversion via non-adiabatic transitions to the electronic ground state. The proton transfer occurs 46, 70, and 91 fs after the initial ionization from a 1b1, 3a1, and 1b2 orbital, respectively. The initial valence ionization induces strong vibrational excitations in the surrounding water molecules, leading to a considerable increase in the local effective temperature. The created heat diffuses into the liquid environment on a timescale of several hundred femtoseconds. We compare the results using two different embedding schemes, subtractive and electrostatic embedding, and find overall very similar dynamics.