What is the ruling on a person taking money from others to invest it with a third party unknown to them, with a promise of a 20% profit share that is subject to increase and decrease, and then keeping for himself whatever exceeds this percentage without the knowledge of the money owners or the investor?

There are two issues related to Mudarabah (definition) (Islamic partnership):

First: In a Sharia (definition)-compliant Mudarabah, it is not permissible to guarantee the capital or to agree on a specific percentage of the capital as profit. If "a profit margin of about 20% of the capital, subject to increase or decrease" implies guaranteeing the capital or stipulating a specific percentage of profit, then this invalidates the Mudarabah. However, if it is merely an estimate of expected profit without stipulation, and the capital providers bear the loss, then there is no harm, provided there is an agreement on a common percentage for dividing the profits (not from the capital), such as one-third for the Mudarib (entrepreneur) and two-thirds for the capital providers. If this is not agreed upon, the Mudarabah is invalid, and all profit belongs to the capital provider, while the Mudarib receives a wage equivalent to his work.

Second: If the capital providers entrust their funds to the Mudarib for him to work with personally, he is not permitted to hand them over to another party without their permission, or without a general authorization to invest the money. If they authorize him or permit him, then the profit is divided between him and the capital providers according to their agreement. Then, he divides his share of the profit with the second Mudarib according to their agreement. However, if they did not authorize him and did not permit him, he has no right to the profit if it occurs (it belongs to the capital providers and the second Mudarib), and if a loss occurs, the first Mudarib guarantees it from his own money.