rejuvinate vacuum hoses

I am hoping one of you know something to spray, rub or apply somehow to the vacuum hoses to make the supple from the brittle state they are in now

I am in the process of replacing every hose in the car. It is just at the back of the A/C heater switch has 7 vacuum lines. That form a plug. I am trying not to damage the plug and would like to extend their lives. I do not remember seeing another tubing plug anywhere.
But now to my question that I need info on. Referring to the pictures, I have no idea what the large round black plastic device is. It has two hose nipples. The device next to it, is that the Water Shut Off valve?? If so, I imagine I need to route the heater hose thru there?

I do really appreciate all the help I have been receiving. I am this | | close to getting the A/C to run and that is a necessity here in the Valley of the Sun

Ed