The OG Invite Restrict module is a simple module that limits the OG invitation page to only accept current usernames - not email addresses. This has the effect of only being able to invite current users of the site into the group.
Furthermore, the module adds autocomplete to the username field (be sure to give anyone with access to this page the "access user profile" permission).
Once installed and enabled, be sure to visit admin/user/permissions and give the "can be invited to join groups" permission to the desired roles. Most sites will want to select just "authorized users".
If the RealName module is enabled, OG Invite Restrict will utilize it.