The problem of dipole transition-matrix element calculation for optical transitions in multiply charged one-electron diatomic quasimolecules with unequal nuclear charges Z1 and Z2 has been stated and solved. The quasimolecule Z1 e Z2 is a unique example of a two-center system for which the energy terms and dipole transition moments have been calculated precisely in the frame of a nonrelativistic approach. Particular examples for the optical transitions with Z1 =1.5,2,2.5,3 and Z2 =1 and with the principal quantum number of the united ion nu =1,2,3,4 have been tabulated. The scaling rules make it possible to determine the matrix elements for quasimolecules having nuclear charge ratios such as 2:1, 3:1, 3:2, and 5:2. Zeros at intermediate R and zero limiting values at large R are the highlighted features of the matrix elements. The heteronucleus case generates a large number of asymptotically forbidden transitions corresponding to transitions of an electron from one ion to another.