yep
Move the eggs to the smaller tank, you don't want to disturb main tank including the parents by moving any of the fish, otherwise they might not breed again..
Now as for moving the parents or is their job over.
It really depends on the situation.
A lot of Angels do take care of the young but it is almost imposible to tell which will and whch will not. While others will take care of fyes for a day or two and then eat them. Plus there are other fish to worry about when the flyes begin to swim.
The only way to ensure no one eats the babies is to put them into another tank.
