Since hte male would pass on white egg genes, you can pretty much discount his impacting the colour with the addition of coloured egg genes. At best his genes will dilute colour of the offsprings' eggs.
So, it will depend on which egg genes she passes to each offspring. Let's assume she has only one blue egg gene--in that case only half her offspring would inherit it (as compared with all of them is she had 2). And for convenience, let's assume that there is only one brown egg gene instead of the many that there are. Once again, if she only has one copy, half her offspring will inherit vs all if she has two.
Okay, to combine those two, half the offspring would inherit one blue egg gene, and of those hald would inherit the brown egg gene as well, while the other half would not. So, of the half that inherited the blue egg gene, half (or a quarter of all offspring) would lay green eggs and an equal number would lay blue eggs.
Of the other half that did not inherit the blue egg gene, half will have inherited the brown egg gene, and thus lay brown eggs (a quarter of the total offspring) and half will not inherit that gene and will lay white eggs.
Now let's complicte matters--about half the offspring are male, and while they have the genes for laying whichever colour of egg, if they do lay, you'll make your fortune, lol.
Quick summary: 1/4 each of blue, green, brown & white if both egg colour genes are het. If you get significantly more blue or green eggs, then she was probably homozygous for the blue egg gene. Likewise if you get only brown & green eggs, she is homozygous for the brown egg gene.