Is it permissible to take what the zakat payer has paid from his own money when purchasing shares for orphans, then sell them and give the profit to them?

Your purchase of shares on behalf of orphans falls into two categories:

1. With the permission of their guardian: The profits from the shares belong to them, and the capital you paid is yours, because you lent them the price of the shares. It does not matter that the shares are in your name as long as the purchase was with the guardian's permission and for their benefit.

2. Without the permission of their guardian (unauthorized purchase - شراء الفضولي): This action is contingent upon their guardian's permission. If he permits it, the purchase is valid, and you take the capital while the profits remain theirs. If he does not permit it, then all the shares become your responsibility (meaning their value belongs to you). It is preferable to refer to the Sharia court in this matter to resolve any dispute.