Is it permissible for me, according to Sharia, to take the remaining amount after agreeing with the client on a certain sum, then negotiating a lower amount with my colleague who does the design?

If you have agreed with him upon a known wage, then you are entitled only to what you both agreed upon, and the surplus must be returned to its owner. If you did that work as a charitable act, then you are entitled to nothing except what the man willingly gives you. It is permissible for you to take the remainder if you contracted with him to design something for a specific amount, and then someone else accepted it from you for a lesser amount.