The shrimp in the picture above are not L. rathbunae , but that is of little consequence since the picture was lifted from Horozbina (where it was misidentified) and isn't of your friend's shrimp.
A review of the peppermint shrimp complex within the genus Lysmata was conducted in 2006 by Andrew Rhyne. He gave a lecture at IMAC in which he detailed the morphological differences. He also suggested that most of the peppermint shrimps in the trade are misidentified, as no formal review of the group had ever been conducted. Rathbunae has bright, contrasting red stripes along the body. I have a PDF of the publication if you'd like to review it.
Rathbunae is sometimes chosen for captive culture because its larval period is about half of some of the other shrimps in the complex (Wittenrich 2002).