[en] This is a sequel to the previous paper on the relation between Parker-Fulling's approach and DeWitt's another one to a quantized scalar field in a special Bianchi-type I universe. An attempt is made to dissolve such a complexity in our previous stipulation of DeWitt's two vacuum states connected causally that the resulting elementary solution includes an information at the two limiting epochs appearing in it. By virtue of the refined stipulation which is based on a suitable extension of the space-time manifold, it is shown that the revised elementary solution becomes identical with ours relying on the former approach, whose coincidence limit is a local quantity (as it should be so). Several problems related to the above procedure are also touched upon. (auth.)