What is the best way to move the flock?

Hello everyone! I am completely new to chickens. My neighbor bought 5 chicks in April and decided they no longer wanted them. My husband and I knew that we wanted chickens eventually (like next year) but decided to take these girls on. We are in process of building a chicken coop and we have water and food in our garage for them. They go back to where the neighbor had them every night (we think) and come back to our place every morning. They are starting to expand their free range area and we are worried about their safety.
We are looking at another week or 2 before we are ready to introduce them to their new home. My question is....how the heck do get them gathered up into their new space? Do we wait until the coop is finished and keep them penned up in the run for 1-2 weeks before letting them out again?
What if they start laying eggs before the coop is done....will it be harder to transition them?
What would you do? Any advice would be super helpful.
(If it makes any difference we are located a few miles north of Syracuse NY)
Thanks in advance!!

They should be moved in when the coop is finished. Keep them locked in the coop for 2-3 days, then allow them into the run. If you plan on free ranging, wait about 1 week to let them back out of the run.

Well...the girls were introduced to their new coop yesterday evening. Only one of them has started laying (just last Thursday!!) and I was pleasantly surprised to see that she laid an egg today IN the nesting box. I was worried that she would be stressed in the new environment. They seem to like it so far. I know they want out becuase they have been free ranging since late May/early June. Hopefully they will adjust and the others will start laying soon! I just love this website anf the endless amounts of info anf people willing to help out. Makes this so much easier!