The Holy Spirit, for Muslims, is a name for the angel Gabriel (PBUH), and a name for Allah’s (S.W) inspiration and His support for his prophets.

The Holy Quran calls the angel Gabriel (PBUH) as the Holy Spirit. Allah (S.W) Says, “Say, the Holy Spirit has brought the revelation from thy Lord in Truth” (Holy Quran 16:102), also, Allah (S.W) says, “Then will Allah say: "O Jesus the son of Mary! Recount My favour to thee and to thy mother.

Behold! I strengthened thee with the holy spirit.” (Holy Quran 5:110) In addition, the Holy Quran calls Allah’s (S.W) inspiration to his prophets as Spirit.

Allah
(S.W) says, “And thus have We, by Our Command, sent inspiration to thee.” (Holy Quran 42:52), He also says, “Raised high above ranks (or degrees), (He is) the Lord of the Throne (of Authority): by His Command doth He send the Spirit (of inspiration) to any of His servants he pleases.” (Holy Quran 40:15)

It is important to mention, that what the Holy Quran says about the Holy Spirit is not far from what the Bible says, but it does not agree with the Constantinople Council meaning.
The Holy Bible mentions that various creatures hold the name ‘Holy Spirit’:

1. The human spirit, which Allah (S.W) creates in his creations, is Allah’s (S.W) Spirit, which He creates in them. “And to the spirits of the righteous made perfect.” (Heb. 12/23), “ when you take away their breath, they die and return to their dust.

When you send forth your Spirit, they are created, and you renew the face of the ground.”
(Psalms 104/29-30) Allah (S.W) gave life to Adam by the same spirit. “and breathed into his nostrils the breath of life, and the man became a living creature.” (Gen. 2/7).

This spirit is called ‘the spirit of Allah (S.W)’ because it came from Allah (S.W), and to Him it will return. “And the spirit returns to God who gave it.” (Ecc. 12/7).

2. The inspiration that the angels carry to prophets, “David himself, in the Holy Spirit, declared” (Mark 12/36), also “ And his father Zechariah was filled with the Holy Spirit” (Luke 1/67), Peter said, "Brothers, the Scripture had to be fulfilled, which the Holy Spirit spoke beforehand by the mouth of David.” (Acts 1/16).
Allah (S.W) called the prophets and what they bring of this inspiration as the Holy Spirit, as He said scolding the people of Israel, "You stiff-necked people, uncircumcised in heart and ears, you always resist the Holy Spirit. As your fathers did, so do you. Which of the prophets did not your fathers persecute?” (Acts 7/51-52)

3. The Holy Spirit is also a name for the aid and wisdom, which Allah (S.W) gives to His prophets and others, and the angels or others can deliver it. Jesus said, “But if it is by the Spirit of God that I cast out demons.” (Matt. 12:28) and what Pharaoh said to his servants, when he was looking for a wise man.

"Can we find a man like this, in whom is the Spirit of God?” (Gen. 41/38) “ Now there was a man in Jerusalem, whose name was Simeon, and this man was righteous and devout, waiting for the consolation of Israel, and the Holy Spirit was upon him.” (Luke 2/25), also, the Holy Spirit supported the disciples on the fiftieth day “ And they were all filled with the Holy Spirit and began to speak in other tongues as the Spirit gave them utterance.” (Acts 2/4).

This is the same as what the prophet Haggai said, “My Spirit remains in your midst. Fear not.” (Haggai 2/5)

4. The strong wind also called the Holy Spirit. Describing the destroying wind, the Torah says,
“The grass withers, the flower fades when the breath of the LORD blows on it.” (Isaiah 40/7), the same is in Genesis, “ And the Spirit of God was hovering over the face of the waters.”
(Gen. 1/2), there is a mistranslation in this passage that leads to this confusion. The passage, as the great critic Espinoza said, ‘means a strong wind came from God, and ceased darkness.’

Moreover, relating the spirit to Allah (S.W) in the last two passages is glorification and esteem, not deifying, as it says, “ The mountains of God” (Psalms 36/6)

Those who worship the Holy Spirit do not accept all the meanings that I have mentioned. They do not accept the idea that the Holy Spirit is just a power or angel from Allah (S.W).

The Holy Spirit, according to the Christian concept is God, is the third hypostasis of the Trinity. What is the Holy Spirit according to their concept? What evidence do they have for considering him as a God? When did that happen? In 381 C.E, by the order of the Emperor Tedious, the Council of Constantinople formed, to discuss Bishop Macedonius’ belief.

He denied the divinity of the Holy Spirit; and he believed what the Holy Books mentioned about him. He believed that, “The Holy Spirit is a divine work spread in the world, not a divine person who is different from the Father and the Son”, and, “He is like all the creations”, and he saw him as a servant of the Son just like one of the angels.

One hundred and fifty priests attended this council. These priests decided to deprive Macedonius of his office, and they made one important decision never made by the church councils before, which was deifying the Holy Spirit.

They considered him as a complement to the Trinity. They said, “We have no other meaning for the Holy Spirit except the Spirit of God, God is nothing except his life, and saying that the Holy Spirit is a creation, is the same as saying that
God is a creation.”

Priest Yasin Mansor said, “The Holy Spirit is the eternal God, he existed before the creation, and he is the creator of everything, able to do anything. He is present everywhere, and he is the everlasting and the unlimited”.

He also said, “The Holy Spirit is the third hypostasis of the Trinity. He is not just a power or characteristic, but a real self, a living person, and a distinct divine being.

He is not separate; he is a divine unit different from the Father and the Son, but equal to them in power and position, sharing with them the basic and the same divinity.

Christians refer to John’s Gospel when talking about the divinity of the Holy Spirit: “God is spirit” (John 4/24). They also believe that he is the spirit that existed from the beginning of creation, “In the beginning, God created the heavens and the earth.

The Spirit of God was hovering over the face of the waters.” (Genesis 1/1-2). Many other passages also mention spirit, God spirit,
or the Holy Spirit.

SOURCE: https://www.muslimhowto.com/2020/03/islam-perspective-divinity-of-holy-spirit.html