As S. aureus is a Gram+ it doesn't exhibit any outer membrane. For membrane fraction preparation, cells have to be digested with lysostaphin (to degrade peptidoglycan and promote cell lysis) then sonicated (or other mechanical treatment) and then cellular fractionation is made through centrifugation. You may inspire from the following paper:
Hi, here is a paper we published about how to overexpress and purify one receptor protein of S. aureus. Hopefully, you can find some useful information from it. Thanks.
"Green Fluorescent Protein (GFP)-Based Overexpression Screening and Characterization of AgrC, a Receptor Protein of Quorum Sensing in Staphylococcus aureus"