What is the relatedness of sisters in a haplodiploid system if you mate virgin queens with 1 of their sons
This question may not be duplicate but I would reconmmend reading the answers of this question first How to calculate relatedness in haplodiploid organisms (mainly full sisters and full brothers)?

I think an image is worth a lot of words so here it is:


To calcul relatedness, I used the formula 
$ \text{relatedness} = \ce{prop_{mother}} \times \ce{shared_{mother}} + \ce{prop_{father}} \times \ce{shared_{father}}$ 

The little trick here is that we know the father (son of queen) is unique, so we can focus on either of the two possible son of the queen. This gives us a 0.875 relatedness between sisters with a father being the son of the mother.
I hope it is clearer now.