If he is an EE with a blue gene, hens that lay brown eggs will give you pullets that lay green eggs; hens that lay white eggs will give you pullets that lay blue eggs.
If your EE rooster has a brown coating gene when you breed him to brown egg laying hens, you will get some pullets that green eggs and some pullets that lay brown eggs; if you breed him to a hen that lays white eggs you will get some green eggs and some cream/pale brown eggs.
If your EE rooster has a brown coating gene when you breed him to brown egg laying hens, you will get some pullets that green eggs and some pullets that lay brown eggs; if you breed him to a hen that lays white eggs you will get some green eggs and some cream/pale brown eggs.