Three main causes for quail to stop laying:
1) Stress
2) Improper diet
3) Too little light
I'd be more strange if they continued to lay after being moved, as that is one thing that is almost certain to stress them. However, it seems they usually start laying again about 3 weeks after being moved, if that is the only problem. So either your quail are just about to start laying again, or there is some other cause why they don't.
If they get ~14 hours of daylight, lack of light is not likely to be the cause. So, for the diet - are they getting something with at least 24% protein? Do they get extra calcium? Are there vitamins in their feed? Do they always have water? If the answer to all of these is 'yes', let's go back to other things that cause stress.
One thing could be your male to female ratio. Usually people say 3 or 4 to 7 females for each male. Lower number of females can cause over breeding. If they have very much room - like, if they live in an aviary or such - 2 females for a male might be fine. But if they only have the usual 1-2 square feet per bird, it's probably not ideal. Other causes of stress could be predators around their cage, parasites and similar.