Studies of parity (P) and time-reversal (T) symmetry violations using molecules are important and attractive because they are complementary to the high-energy tests of physics beyond the Standard Model of elementary particles. The focus of our present work is to surpass the current accuracies of the quantity X, an enhancement factor for the nuclear Schiff moment (Q), and the nucleon electric dipole moments for the (TlF)-Tl-205 molecule. We obtain X = 6856 a.u. using a relativistic coupled-cluster singles and doubles and perturbative triples (CCSD(T)) approach. This new value of X improves the upper limits for Q and the proton EDM by about ten percent over the previous ones. [GRAPHICS] .