Cooler in the housing, how to connect?

Hi all. Recently built a computer, have everything set up, but there is a delay with the power supply hasn't arrived yet, so wait.
All case gamemax g536. It will include 2 fans blowing on the front panel, and a cooler on blowing behind.
Need help connecting)
In General, this cooler has a button, like the built-in fan controller. As I understand it, when the system is running - just turning cooler. When you press the button on the fan control, a fan should start spinning faster.

Now on the wire. with two front coolers is a single wire 4 pin(for BP), With the rear of the cooler is only full of a small connector, like a 3 pin. And two front too, these are 3 pin and they all saadany among themselves, and head to the button with the fan controller. And there is another 4 pin wire that is sticking most likely with the buttons on the fan controller.
I know that is a little complicated) But might be able to help)
Tell me how to connect everything? And that button would affect all 3 of the cooler ?
Thank you.