A number of scriptures in John 14 and 15 in which Jesus promises to send the Holy Spirit would seem to render it entirely impossible that Jesus is the Holy Spirit:
16 And I will ask the Father, and he will give you another advocate to help you and be with you forever—
John 14:16
26 But the Advocate, the Holy Spirit, whom the Father will send in my name, will teach you all things and will remind you of everything I have said to you.
John 14:26
26 “When the Advocate comes, whom I will send to you from the Father—the Spirit of truth who goes out from the Father—he will testify about me.
John 15:26
It would seem that Jesus is indicating that the Holy Spirit is an Individual entirely separate and different from Himself. However, a similar thing occurs when Jesus refers to the Son of Man.
“The Son of Man will send forth His angels, and they will gather out of His kingdom all stumbling blocks, and those who commit lawlessness.”
Matt. 13:41
“The Son of Man is going to be delivered into the hands of men and they shall kill Him, and He will be raised on the third day.”
Matt. 17:22-23
“Truly I say to you, that you who have followed Me, in the regeneration when the Son of Man will sit on His glorious throne, you also shall sit upon twelve thrones, judging the twelve tribes of Israel.”
Matt. 19:28
“Behold, we are going up to Jerusalem; and the Son of Man will be delivered to the chief priests and scribes, and they will condemn Him to death, and will hand Him over to the Gentiles to mock and scourge and crucify Him, and on the third day He will be raised up.”
Matt. 20:18-19
“But when the Son of Man comes in His glory, and all the angels with Him, then He will sit on His glorious throne.”
Matt. 25:31
When Jesus refers to the Son of Man in these scriptures it also seems like He is referring to an entirely different person from Himself. However, in Matthew 16:15 Jesus identifies Himself to be the Son of Man:
13 When Jesus came to the region of Caesarea Philippi, he asked his disciples, “Who do people say the Son of Man is?”
14 They replied, “Some say John the Baptist; others say Elijah; and still others, Jeremiah or one of the prophets.”
15 “But what about you?” he asked. “Who do you say I am?”
16 Simon Peter answered, “You are the Messiah, the Son of the living God.”
17 Jesus replied, “Blessed are you, Simon son of Jonah, for this was not revealed to you by flesh and blood, but by my Father in heaven.
Matthew 16:13-17
It is clear from verse 15 that Jesus is Himself the Son of Man and that there is no separate or different Son of Man.
It would seem that in the verses in John 14 and 15 in which Jesus refers to the Holy Spirit in the third person that He is doing the same thing as when He referred to Himself as the Son of Man in the third person.
Although He speaks of Himself as the Holy Spirit in the third person, He indicates in John 14, that He Himself is the Holy Spirit. For example, in John 14:7 Jesus tells the disciples that the Holy Spirit lives with them:
17 the Spirit of truth. The world cannot accept him, because it neither sees him nor knows him. But you know him, for he lives with you…..
John 14:17
As the Holy Spirit only came on Pentecost and Jesus was the One Who was living with them at that time and the One that they knew, this indicates that Jesus Himself is the incarnate Holy Spirit.
In John 14:18-20 He says:
18 I will not leave you as orphans; I will come to you. 19 Before long, the world will not see me anymore, but you will see me. Because I live, you also will live. 20 On that day you will realize that I am in my Father, and you are in me, and I am in you.
John 14:18-20
Notice that at the end of verse 20 He tells them that He will be in them. Obviously there is no way that He could come and physically climb inside of them to live in them. The only way that He could be in them would be in the form of a Spirit. We know as Christians that the Holy Spirit is the One Who is in us. We are the temple of the Holy Spirit.
In verse 18 Jesus is telling the disciples that He will come to them. This happened on the day of Pentecost when the Holy Spirit came down and filled the disciples. He tells them that He will come to them in a way that the world cannot see Him. The world cannot see Jesus living in a Christian as the Holy Spirit.
The apostle Paul seems to be the person who fully understood that the Holy Spirit is Jesus Himself. He described it as a mystery:
24 Now I rejoice in what I am suffering for you, and I fill up in my flesh what is still lacking in regard to Christ’s afflictions, for the sake of his body, which is the church. 25 I have become its servant by the commission God gave me to present to you the word of God in its fullness— 26 the mystery that has been kept hidden for ages and generations, but is now disclosed to the Lord’s people. 27 To them God has chosen to make known among the Gentiles the glorious riches of this mystery, which is Christ in you, the hope of glory.
Colossians 1:24-27
This is the glorious mystery that the Holy Spirit is Jesus Himself and that He lives within the Church. Years ago I asked the Holy Spirit what I should call Him because I thought it seemed very formal to call Him Holy Spirit. The answer came back as clear as anything. He said: ‘Jesus.’
In Colossians 1 the apostle Paul distinguishes between Jesus’ physical body and the church as Jesus’ body:
22 But now he has reconciled you by Christ’s physical body through death to present you holy in his sight, without blemish and free from accusation—
Colossians 1:22
24 Now I rejoice in what I am suffering for you, and I fill up in my flesh what is still lacking in regard to Christ’s afflictions, for the sake of his body, which is the church.
Colossians 1:24
It is clear that Paul understands Jesus to be living inside the church as the Holy Spirit and that the Church is His body. A few verses earlier Paul described the Son of God:
12 and giving joyful thanks to the Father, who has qualified you[f] to share in the inheritance of his holy people in the kingdom of light. 13 For he has rescued us from the dominion of darkness and brought us into the kingdom of the Son he loves, 14 in whom we have redemption, the forgiveness of sins.
15 The Son is the image of the invisible God, the firstborn over all creation. 16 For in him all things were created: things in heaven and on earth, visible and invisible, whether thrones or powers or rulers or authorities; all things have been created through him and into him. 17 He is before all things, and in him all things hold together. 18 And he is the head of the body, the church; he is the beginning and the firstborn from among the dead, so that in everything he might have the supremacy. 19 For God was pleased to have all his fullness dwell in him, 20 and through him to reconcile to himself all things, whether things on earth or things in heaven, by making peace through his blood, shed on the cross.
Colossians 1:12-20
In verses 15-18 Paul is clearly describing Jesus as He pre-existed as the Holy Spirit. Then In verses 18-20, Paul is describing the Holy Spirit after He became incarnate as Jesus.