Is it permissible to cash a post-dated check for $600 USD, with a maturity date two months from now, in exchange for receiving $550 USD immediately from the money exchanger?

It is not permissible to cash a post-dated check for less than its full value immediately, as this is a usurious transaction. This is because the exchange office lends you a smaller amount in return for recovering the full value of the check upon its maturity. This falls under usury, which the Quran warned against, and its perpetrator was cursed by the Prophet, peace be upon him.