If you have your Groupsite membership invitation settings set to "allow all Groupsite members to invite new members to this group" (which you can do by going to the MANAGER tab then selecting the "Invite Members" subtab and selecting it from the "Invitation Options" drop-down.) then here is how you can see who has invited who:
Click on the MANAGER tab then the 'Pending Members" subtab,
you can see who invited who under the "inviter" column.
If they have already joined the group, then select the "Manage Members" subtab and in the "Source" column next to the members name, roll your mouse over the word "invited" and a pop-up will show the name of who invited them.
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