In the time of Aristotle, it was widely believed that the human soul entered the forming body at 40 days (male embryos) or 90 days (female embryos), and quickening was an indication of the presence of a soul.
Muslims think that the soul is breathed into the fetus after one hundred and twenty days of conception.
What are the views of Christian and Jewish?

“Before I formed thee in the belly I knew thee;”. Jeremiah 1:5

“Thine eyes did see my substance, yet being unperfect; and in Thy book all my members were written, which in continuance were fashioned, when as yet there were none of them.” Psalm 139:16

Quoting the scriptures is the most honest answer I can give you, friend. As you can see, I don’t know of a scripture that more specifically answers your question. But to me, knowing the character and eternal awesomeness of God, it gives me the idea that both soul and spirit are endowed upon the new human at the moment of conception.

Thank you. But the bible shows different functions of the soul and spirit in Mary’s praise of the Lord:
“And Mary said, My soul magnifies the Lord, and my spirit has exulted in God my Savior.” Luke 1:46-47
Is it the same in a fetus ?

Yes, they are distinct things. I could only suppose that they would be as distinct to a fetus as to anyone else since I can’t imagine how a soul and spirit could at any point be the same thing. I don’t think that one of them could give rise to the other since the spirit is immortal but the soul is mortal.

Different (newer) translations of the Bible often use spirit and soul interchangeably, which unfortunately adds to the confusion about this subject. It is impressive that you noticed this distinction while most of the Christians I’ve had this conversation with go through their lives assuming that soul and spirit are only synonyms.

In the King James Version, which is the only English translation I study from, the Greek word psuche is translated as soul, and pneuma is translated as spirit. Psuche is the animating life force and basic sentience which all living creatures have. If Freud had been interested in the scriptures, I think he might have said that that this would compose the id and ego part of the mind. Personally, I don’t like Freud, so I just say that the mind, psuche, and soul are different words for the same thing. The pneuma, is a bit more mysterious to me, as I suppose it should be. Only human beings have this pneuma, which endures after our bodies perish. I like to associate the pneuma/spirit with that special part of our being we figuratively call our “heart”, which also I think Freud would have associated with his superego. The spirit is how it is possible to dwell with God through the mediator, Christ, for “No man hath seen God [the Father] at any time,” (John 1:18), and again “God is a spirit: and they that worship Him must worship Him in spirit and in truth” (John 4:24).

The Quran says about the creation of the fetus;
Then we created the sperm a leech, so we created the clot, so we created the embryo as bones, then we clothed the bones with flesh, then we created it in another way, so God blessed the best of creators.

Prof. (Dr.) Keith Moore, of Embryology in Canada, said that most of the information concerning embryology mentioned in the QURAN is in perfect conformity with modern discoveries in the field of embryology and does not conflict with them in any way.

If the bible doesn't say that, then it is not true! It will remain a believe and I don't see the benefits of believing it's true.