The 1874 RLDS edition accidentally replaced the determiner that with the here in Ether 15:11. We have already seen this kind of change numerous times in the history of the text. For some examples where Oliver Cowdery and the 1830 typesetter mixed up these two determiners, see under Helaman 14:20 and 3 Nephi 1:12. For another case where the 1874 typesetter replaced that with the, see under Mormon 9:11 (in that case, the replacement occurred in the phrase “that same God”, which also involves the word same).
Either reading, of course, is possible here in Ether 15:11. For instance, elsewhere in the text we have two instances of “same place” followed by a where-clause. In one case, the determiner is that; in the other, it is the:
In fact, the second passage shows the tendency, once more, to replace that with the (see under Alma 58:17 for discussion). Thus the critical text will follow the earliest reading here in Ether 15:11, “it was that same hill”.
Summary: Maintain in Ether 15:11 the determiner that before same, the reading of the earliest extant text: “it was that same hill where my father Mormon did hide up the records”.