We didn't have an Exchange server on site with everyone's mailbox, and this was a requirement for migrating from GroupWise to Exchange Online.

Set-ProxyAddresses.ps1

$users = get-aduser -Filter * -Properties proxyAddresses,EmailAddress

foreach ($u in $users) {
    if (!($u.proxyAddresses -contains "SMTP:$($u.EmailAddress)")) {
        $u.proxyAddresses.Add("SMTP:$($u.EmailAddress)")
        Set-ADUser -Identity $u.SamAccountName -Add @{ 'proxyAddresses' = $($u.proxyAddresses) }
    }
    else {
        Write-Host "$($u.name) already had the correct proxyaddresses"
    }
}