This verse is most often cited as an explanation for the reason that the people are praying to Jesus. (See commentary on verse 18.) However, here it is about the twelve.
First, Jesus acknowledges his Father as the source for conferring the Holy Ghost, not himself. Second, he notes that the gift of the Holy Ghost comes because of belief in him: “Thou hast given them the Holy Ghost because they believe in me.” God is the source of the gift, but a prerequirement for receiving it is belief in Jesus Christ (or, in Nephite terms, in the Atoning Messiah).
What evidence is there of the twelve’s belief? The evidence is that they are praying to Jesus. They do not believe in Jesus the man or in Jesus the resurrected man. They believe in Jesus as Messiah, Jesus as Yahweh. They have believed that he would come, and they now believe him to be here.