I am not sure if this is possible for her to do, but when one of my chickens were eating the eggs I sent them all out of the coop to free range. Personally I think she was bored. It was the middle of the winter and I was trying to keep them in the coop. I also added oyster shell to the feed to make the eggshell stronger.
I am not sure what made the hen stop but this did work for me. I have heard that once this starts it is really hard to make them quit. One website talked about culling the guilty hen but I couldn't bear to do it.
I hope somebody on here has more concrete advice because I am just speaking from my experience.
You're on the right track. It's almost always due to boredom. First, they need to have plenty of room. Overcrowding is the number one reason. Second, they need to have something to keep them busy. Do a websearch for chicken or poultry enrichment, and you'll find all kinds of ideas. Here are a few: hang a head of romaine from a rope, for them to pick at, give them plenty of deep, clean bedding to scratch around in, evergreen boughs to hide in and pick at, baffles or sight barriers in the coop to allow for hiding places, things to jump over or go around, a flake of nice green leafy hay or alfalfa, I use a hay rack to keep it up off the floor, a handful of mealworms thrown in the litter or in a big shallow tub, with some litter, for them to scratch around for, or better yet, a few dozen crickets from the pet store. Scatter dummy eggs around, for them to peck at and realize that there is no benefit to it. All of these things need to be changed frequently, to prevent them from getting bored with the same old thing.
It's true that once started, it is very hard to control, and one bird can soon teach it to all of the others. If you catch it early, before it becomes an ingrained habit, you can correct it, but once it's become a habit, it is extremely difficult to break it and the only answer is to cull. You will not ever be able to introduce new birds to the same flock, because they too will learn it. Like most things, it is much easier to prevent in the first place.
If she can she needs to get out there and collect eggs frequently for a few days. If the eggs are not there they can not eat them and this will help break that cycle. Plus put false eggs into the nest boxes. If they peck at these they won't find anything interesting and will become bored with it quickly. Tell her good luck!
My friend has one of those nestboxes where the floor is on a slight incline and the eggs roll out the back of the nest into a little area where she can gather them up and the hens can't reach them anymore. Would something like that work for a hen that pecks eggs?
I keep a couple of wooden eggs in the nests. Pecking on those is discouraging and they will eventually give up.
I've found that an especially critical time is as the pullets come into lay - they are curious about those round things that keep coming out of their hind ends and poke and peck at them. All it takes is an accidental break, a taste, and they are hooked!
Frequent collection is also good - do you have any neighbors who can help you collect eggs while you are at work or away? Remember that kids LOVE to collect eggs.