Paul said "Did you receive the Holy Spirit?"

While Apollos was in Corinth,
Paul traveled through the interior of the country
and down to Ephesus where he found some disciples.
He said to them,
"Did you receive the Holy Spirit when you became believers?"
They answered him,
"We have never even heard that there is a Holy Spirit."

-- Acts 19:1-8

Even more, what the Father gives us when our prayer is united with that of Jesus is "another Counselor, to be with you for ever, even the Spirit of truth." This new dimension of prayer and of its circumstances is displayed throughout the farewell discourse. In the Holy Spirit, Christian prayer is a communion of love with the Father, not only through Christ but also in him: "Hitherto you have asked nothing in my name; ask, and you will receive, that your joy may be full."

-- CCC 2615

Jesus is Christ, "anointed," because the Spirit is his anointing, and everything that occurs from the Incarnation on derives from this fullness. When Christ is finally glorified, he can in turn send the Spirit from his place with the Father to those who believe in him: he communicates to them his glory, that is, the Holy Spirit who glorifies him. From that time on, this joint mission will be manifested in the children adopted by the Father in the Body of his Son: the mission of the Spirit of adoption is to unite them to Christ and make them live in him:

The notion of anointing suggests . . . that there is no distance between the Son and the Spirit. Indeed, just as between the surface of the body and the anointing with oil neither reason nor sensation recognizes any intermediary, so the contact of the Son with the Spirit is immediate, so that anyone who would make contact with the Son by faith must first encounter the oil by contact. In fact there is no part that is not covered by the Holy Spirit. That is why the confession of the Son's Lordship is made in the Holy Spirit by those who receive him, the Spirit coming from all sides to those who approach the Son in faith.

-- CCC 690