Problem with missing users in group membership page in Sharepoint

Some time ago we faced with strange problem: on one of Sharepoint 2013 sites some users were not shown in their groups’ membership page (Site settings > Users and groups: http://example.com/_layouts/15/people.aspx?MembershipGroupId=groupId). Such users were able to login to Sharepoint and had all necessary permissions, but they didn’t appear on this page. Also need to notice that this site was migrated from SP2007. When I checked groups of the missing user via PowerShell:

   1: $u = Get-SPUser -Id "loginName" -Web http://example.com

   2: $u.Groups

they were properly returned. Also it worked as expected when I checked it in opposite way: check members of the group:

   1: $web = Get-SPWeb http://example.com

   2: $g = $web.SiteGroups["Foo"]

   3: $g.Users

User was shown there as well. And when I checked permissions via the following useful script which shows both permissions granted explicitly to the user and permissions granted via groups:

   1: $url = "http://example.com"

   2: Get-SPUser -Web $url -Limit All | sort-object UserLogin | select UserLogin,

   3:     @{name=”Exlicit given roles”;expression={$_.Roles}},

   4:     @{name=”Roles given via groups”;expression={$_.Groups | %{$_.Roles}}},

   5:     Groups | format-Table -auto

It showed that user has necessary permissions. I.e. the problem was only that user was not shown on the group membership page. In order to fix the issue the following script was used:

   1: $web = Get-SPWeb http://example.com

   2: $g = $web.Groups["Foo"]

   3: $users = $group.Users

   4: foreach ($u in $users)

   5: {

   6:     Write-Host "Fix user" $u.LoginName

   7:     $g.RemoveUser($u)

   8:     $g.AddUser($u)

   9:     $g.Update()

  10: }

It goes through all members of specified groups and then re-add them to this group. After that user appeared on group membership page.