Is it permissible for Ahmed, who resides in city "A" and works for a company that provides housing for non-residents, to apply for the company's housing, knowing that he was previously a resident of city "B" and still owns properties and documents indicating his residency there, despite not currently residing there?

It is not permissible to resort to deception to obtain housing from the company as long as the person resides in the city where the company is located. This is because the company stipulates, for providing housing, that the employee must not be a resident there. Informing the company of something contrary to the truth is a lie and is not permissible.