Some of the links on this forum allow SMF, at no cost to you, to earn a small commission when you click through and make a purchase. Let me know if you have any questions about this.
At my brothers bbq joint they like to present their brisket sliced. I'm not an expert, so all I can tell you is what I observed.
Once finished smoking, the briskets are allowed to rest for about an hour and then placed in the walk-in cooler overnight. The next morning they double wrap them in plastic and the briskets are set to go . . . either to remain in the cooler until needed or placed on a baking pan in the oven to be brought back up to serving temperature before being placed in a food warmer when the restaurant opens.
It's important that you have the brisket on a stiff tray during the process. The plastic wrap never comes off until ready to carve. It will help the meat retain it's juices.