What is the ruling on someone whose colleague gave him money to invest in stocks, and he bought into two specific companies, then speculated in them and took the profit for himself, and after a period his colleague asked him to sell the shares and give him their value, knowing that he did not inform him of what he had done?

An agent does not have the right to act except within the scope authorized by the principal. An agent speculating in stocks for himself without the principal's permission is considered an act of usurpation. Of the profit you earned from the money you took unjustly, only half is rightfully yours, while the other half must be given to the owner of the money.