what is the position of a person who is given with a money to hold it for somebody for a while, then he started bussiness with the money without the ouner's concent. is the profit belong to him or to the ouwner

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

A "Deposit" is an entrustment which a person is obliged to safeguard and give back to its owner. Allaah Says (what means): {Verily! Allaah commands that you should render back the trusts to those, to whom they are due.}[Quran 4:58] Also, it is forbidden to misuse it because misusing it is betraying the trust; Allaah Says (what means): {O you who have believed, do not betray Allaah and the Messenger or betray your trusts while you know [the consequence].}[Quran 8:27]

As regards your question, the scholars differed in opinion with regard to who deserves the profit of the trust, if he trades with it without the permission of its real owner: is he the real owner or the entrusted person? The reason for this difference of opinion here is due to the view whether the profit is due to the capital money or due to the effort. The scholars who are of the view that it is due to the capital money, said that the profit is for the owner of the money. For details, refer to Fatwa 90007. On the other hand, those who are of the view that the profit is due to the effort, said that the profit is for the entrusted person because he is a guarantor of the money, and the Prophet said: “The return (on an asset) is based on liability (i.e. bearing the risks and responsibility).” [Ahmad]

In our view in Islamweb, the second opinion is the preponderant one.

Allaah Knows best.