Egg-eating is a bad habit some birds develop. You want to remove the one hen that is doing it, or else a few others may catch on to the tasty trend.
Sometimes egg-eating can be solved by placing golfballs in the nests. There are many solutions to this problem suggested by many people, if you do a search you will find a TON of info on the subject.
Some people just cull the hen and get it over with, others choose to try and break the habit first and use culling as a last result.
If you decide to rehome her, be sure to be honest and let the next owner know the hen is an egg-eater. Honesty is the best policy. There have been people here, who have bought birds over
ebay only to end up with a flock of egg-eaters, they were dissapointed to say the least.
I wish you well in breaking her of that nasty habit! I would try to separate her while working with her, to avoid her teaching others just how tasty those eggs are.
-Kim