Hi @Toader, Radu X. -ND ,
It been a while since I've looked at foreign security principals but here is a high level overview on how they work.
Members of groups in AD are recorded by the member's DN, this is simple for member's in the same forest, however when member is added from an external domain a foreign security principal is created in the Container of the same off the root. This has the member's SID from the source domain, and the display name or the friendly display name. If remember correctly this is not populated when the FSP is created, it's populated by a background process, so may take some time to populate the display name. Have look at the FSPs in the Container to see if any of them have the display name set.
I quick search found this article https://social.technet.microsoft.com/wiki/contents/articles/51367.active-directory-foreign-security-principals-and-special-identities.aspx
I hope this help, if not, at least you have something to google now.
Gary.