Concise PowerShell AD Group Shadow script from http://ravingroo.com/458/active-directory-shadow-group-automatically-add-ou-users-membership/

Shadow_Group-Generic_basic.ps1

$OU="OU=TheOUName,DC=yourdomain,DC=com"
$ShadowGroup="CN=ShadowGroupName,OU=TheOUName,DC=yourdomain,DC=com"

Import-Module ActiveDirectory
(Get-ADGroup -Identity $ShadowGroup -properties members).Members | Get-ADUser | Where-Object {$_.distinguishedName –NotMatch $OU} | ForEach-Object {Remove-ADPrincipalGroupMembership –Identity $_ –MemberOf $ShadowGroup –Confirm:$false}
Get-ADUser –SearchBase $OU –SearchScope OneLevel –LDAPFilter "(!memberOf=$ShadowGroup)" | ForEach-Object {Add-ADPrincipalGroupMembership –Identity $_ –MemberOf $ShadowGroup}

Shadow_Group-Generic_emailing.ps1

$OU="OU=TheOUName,DC=yourdomain,DC=com"
$ShadowGroup="CN=ShadowGroupName,OU=TheOUName,DC=yourdomain,DC=com"
$WhatIf=$true   #set $true for testing and $false for action

Import-Module ActiveDirectory

Write-Host "Removing non-existent members"
#$RemoveMembers = (Get-ADGroupMember -Identity $ShadowGroup | Where-Object {$_.distinguishedName -NotMatch $OU})    #Fails for more than 5000
$RemoveMembers = ((Get-ADGroup -Identity $ShadowGroup -properties members).Members | Get-ADUser | Where-Object {$_.distinguishedName -NotMatch $OU})   #workaround for 5000 limit
$RemoveMembers | ForEach-Object {Write-Host -NoNewline $_.SamAccountName  ": " ; Remove-ADPrincipalGroupMembership -Identity $_ -MemberOf $ShadowGroup -Confirm:$false -WhatIf:$WhatIf -Verbose}

Write-Host "Adding members"
$AddMembers=(Get-ADUser -SearchBase $OU -SearchScope OneLevel -LDAPFilter "(!memberOf=$ShadowGroup)")
$AddMembers | ForEach-Object {Write-Host -NoNewline $_.SamAccountName ": " ; Add-ADPrincipalGroupMembership -Identity $_ -MemberOf $ShadowGroup -WhatIf:$WhatIf -Verbose}

# Emailing
if ($RemoveMembers -or $AddMembers) {
    $adminEmailAddr="admin1@yourdomain.com","admin2@yourdomain.com"

    $smtpServer="mailserver.yourdomain.com"
    #$from = "$env:COMPUTERNAME <noreply@yourdomain.com>"
    $from = "sender@yourdomain.com"
    $password = "smtppassword"
    $securepass = ConvertTo-SecureString -AsPlainText -String $password -Force
    $credential = New-Object System.Management.Automation.PSCredential -argumentlist $from,$securepass
    
    $subject = "Automated script: ShadowGroup: "+($ShadowGroup -split ',*..=')[1]
    $body="The following shadows applied between: <br>"
    $body+="OU: $OU <br>"
    $body+="Group: $ShadowGroup <br><br>"

    if ($WhatIf) { $body+="TESTING ONLY<br><br>"}

    foreach ($rm in $RemoveMembers) {
        $sName=$rm.SamAccountName
        $body+="Removed $sName <br>"
    }
    if ($RemoveMembers) {$body+="<br>"}

    foreach ($am in $AddMembers) {
        $sName=$am.SamAccountName
        $body+="Added $sName <br>"
    }
    $body+="<br>"

    Write-host "Emailing $adminEmailAddr"
    $textEncoding = [System.Text.Encoding]::UTF8
    try {
        Send-Mailmessage -smtpServer $smtpServer -from $from -to $adminEmailAddr -Credential $credential -subject $subject -body $body -bodyasHTML -priority High -Encoding $textEncoding -ErrorAction Stop -ErrorVariable err
    } catch {
         write-host "Error: Failed to email $adminEmailAddr via $smtpServer"
    } finally {
        if ($err.Count -eq 0) {
            write-host "Successfully emailed $adminEmailAddr"
        }
    }
} else {
    Write-Host "Nothing to email."
}

added smtp auth support.