What is the ruling on my work if a designer created designs for me during his official working hours, which he is not allowed to do, and is the money earned from my trade unlawful?

What you mentioned about the employee's work on designs during official working hours does not prohibit benefiting from them and earning from them, if you use them in what is permissible. The employee's dereliction in his work does not affect the permissibility of benefiting from these designs, and this has no relation to the rule "what is built upon falsehood."