I separate out my extra cockerels into a coop and run by themselves at about 3 months of age. The rest of the flock free-ranges on the property, so the boys had been free-ranging up until they were separated. After they all went into the coop at night, I moved the boys to their new coop. They woke up in their new coop the next morning. The next night, they didn't have a problem going into the new coop at sundown, so I feel like waking up in the new coop helped them identify it as the place where they should roost at night. About a week later, one of the boys managed to escape his run and was in a tizzy that he couldn't figure out how to get back in. I opened the door to the run and stood back and he scurried back into the run himself. That tells me that he's identifed the new coop and run as the place he's supposed to be.
I would move the birds to the new coop at night and let them wake up there in the morning. You can keep them in the new coop for a day if you want, but I open the coop and let them in the run and let them get accustomed to their new digs. At sundown, they should head into the new coop as long as the old coop is not available to them.