The Holy Spirit has variously been interpreted as the angel Gabriel, spiritual power, etc. The Muslim concept is not the third person in the Christian doctrine of the Trinity.
Al Saddi and Kaab wrote, "The Holy Spirit is Gabriel, and his support of Jesus was by being His companion and friend, helping and accompanying Him wherever He went, until He was taken up into heaven."
Ibn Jubair explained, "Spirit of the Holy is the supreme name for Allah and by it Jesus was raising the dead." Ibn Abbas announced, "As it was the spirit which was breathed into Him and the Holy One is Allah so He is the Spirit of Allah."
``As soon as Jesus was baptized, he went up out of the water. At the moment heaven was opened, and he saw the Spirit of God descending like a dove and lighting on him'' (Matthew 3:16)
[John the Baptist said:] `I baptize you with water for repentence. But after me will come who is more powerful than I, whose sandals I am not fit to carry. He will baptize you with the Holy Spirit and with fire.'' (Matthew 3:11)* QN: If the Holy Spirit is the angel Gabriel as believed by Muslims, what does it mean to baptize with Gabriel?