Is it permissible to deal with a brokerage company that allows a client to purchase shares at double their paid-up capital, on the condition that the company pays the remaining amount and collects it deferred with an increased brokerage commission (from 5 to 7 per thousand), and the shares are registered in the client’s name without a late penalty? And is this transaction considered usury (riba)?

There is no objection to a person acting as an intermediary between a seller and a buyer on the stock exchange and taking a commission. There is also no objection to the intermediary paying the remaining amount of the share's value as a loan to the buyer. However, it is forbidden for the intermediary to take a commission on this loan, because it is usury (riba), which is prohibited. Every loan that draws a benefit is usury.