The 1840 edition replaced the determiner his with the, probably accidentally since either reading will work. Elsewhere in the original Book of Mormon text there are eight occurrences of “of his Son” in contrast to eight occurrences of “of the Son” (I count here only instances that refer to the Son of God). There is definitely no reason here in Ether 12:11 for editing the text from “of his Son” to “of the Son”. The 1908 RLDS edition restored the original his to the RLDS text.
Summary: Maintain in Ether 12:11 the earliest reading with his Son rather than the Son in the phrase “in the gift of his Son”.