So we all know our prophets are Muslim hence why they’re all in the Quran for a reason and our prophets. But my main concern is how Christianity or Judaism found some way to make our prophets their figures. For example, Moses (Musa), Adam, Dawood (David), Jesus (Isa Ibn Maryam), Abraham (Ibrahim), Ishmael (Ismaeel) even some of our angels are named after some biblical angels like Gabriel (Jibril), Israfil (Raphael) and Mikael (Michael)
If you want an Islamic answer, I can't help much, but a historical answer is easy.
The Pentateuch, which figures in Moses, Adam, Abraham and Ishmael, is the first five books of the Jewish and Christian Scripture. Tradition ascribes the books to Moses himself and would make it written almost two thousand of years before Mohammed.
The further adventures of the Jewish people are chronicled in the books of Kings and Samuel and summarized in Chronicles which were compiled over a thousand years before Mohammed. That's where David comes in.
The later books of the Torah / Old Testament of the Christians contain references to the angels Raphael (in Tobit, which is only in the Greek Old Testaments, you won't find it in the Bibles of the Protestants) and Michael (in the prophetic part of the book of Daniel).
The New Testament of the Christians contains four books each depicting the life of Jesus Christ. His Incarnation, which is the Christian doctrine that God became man in the Person of Jesus, was foretold by the angel Gabriel, as was the birth of His cousin John the Baptist in the Gospel of Luke (the third book in the Christian New Testament).
Just to come full circle, Michael is also mentioned in a letter included in the New Testament written by the Apostle Jude, talking about Michael and Satan battling over the body of Moses, incidentally referencing a book that isn't in any of our scripture, the Book of Enoch. All the New Testament was finished being written over 500 years before Mohamed's flight to Mecca.
And just as the Koran makes many allusions and contains many stories from Christianity and Judaism, the Christian New Testament makes many allusions and contains many stories from the Jewish Scripture (The Letter to the Romans is full of them).
And to take it one step further, even newer sects, like the Mormons whose scriptures were written 1200 years after Mohamed and 1800 years after Jesus still have the same people figuring into their stories.