Is Jesus giving the Spirit in John 20:22?

Addendum:

The Ezekiel allusion is good. After he spoke to the bones they came to life but "there was no breath in them" v.8. even though he said he would put breath in them. This tells us that the breath he put in them was expended in giving life to the flesh.

So he commanded the wind, after which they had breath.

Receiving the Holy Spirit was a two-step process. 1 They were brought to life when Jesus breathed upon them (by the Spirit of Christ)[2] and then they received the breathe at Pentecost.

Jesus expended his breath (life) upon the cross to give us life. The gift of the Holy Spirit came after.

Just as in the Trinity, there are three Spirits which are one(The Spirit of God, The Spirit of Jesus Christ and the Holy Spirit). They may be referred to interchangeably in the same manner as the Trinity when referring to God, or distinctively when speaking of one of the persons of the Trinity.

Refs

[1]

My answer on how the bread and the word are related supports the two-stage receiving of the Spirit. Just as man does not live by bread (the cross) alone, we live by every word. The cross is where the Spirit of Christ makes us born again, so that we may see the kingdom of heaven. His spirit is expended in giving us life. The Holy Spirit is given so that we may walk in that new life.

[2]

   Php 1:19 For I know that this shall turn to my salvation through your prayer, and the supply of the Spirit of Jesus Christ,