If I need to move an animal. I like to move the male whenever possible so as to cause as little disruption as possible to the female that just littered. Littering and nursing kits is stressful enough as it is without further disruption.
Personally this is one of the reasons I like using runs for breeding since I typically do not need to move anyone. Once pregnancy is established I can just close the male out of the females cage but he can still run over top so they can visit and stay familiar with each other.
Polygamy, colony and pair breeding each have their pluses and minuses.