source: http://www.craig-tolley.co.uk/2016/01/21/wsus-copy-updates-between-groups/

Run the script below, then call it using the following syntax:

Copy-WsusGroupApprovals -WsusServerFqdn wsus.domain.co.uk -SourceGroupName "OldServers" -TargetGroupName "NewServers"

You can optionally specify a port, the default being 8530. You can also specify to use a secure connection. The group names are both case sensitive though.

# ----------------------------------------------------------------------------------------------------------
# PURPOSE:    WSUS - Copy Approvals from one Group to another Group
#
# VERSION     DATE         USER                DETAILS
# 1           21/01/2016   Craig Tolley        First Version
#
# ----------------------------------------------------------------------------------------------------------

#.SYNOPSIS
# Copies all approvals from the specified source group to the specified destination group. 
# Group names are case sensitive. 
# Unless specified the default WSUS port of 8530 will be used to connect. 
function Copy-WsusGroupApprovals
{
    param
    (

    [Parameter(Mandatory=$true)]
    [ValidateNotNullOrEmpty()]
    [String]$WsusServerFqdn,

    [Int]$WsusServerPort = 8530,

    [Boolean]$WsusServerSecureConnect = $false,

    [Parameter(Mandatory=$true)]
    [ValidateNotNullOrEmpty()]
    [String]$SourceGroupName,

    [Parameter(Mandatory=$true)]
    [ValidateNotNullOrEmpty()]
    [String]$TargetGroupName

    )
    
    # Load the assembly required
    try
    {
        [void][reflection.assembly]::LoadWithPartialName("Microsoft.UpdateServices.Administration")
    }
    catch
    {
        Write-Error "Unable to load the Microsoft.UpdateServices.Administration assembly: $($_.Exception.Message)"
        break

    }

    # Attempt the connection to the WSUS Server
    try
    {
        $WsusServer = [Microsoft.UpdateServices.Administration.AdminProxy]::getUpdateServer($WsusServerFqdn, $WsusServerSecureConnect, $WsusServerPort)
    }
    catch
    {
        Write-Error "Unable to connect to the WSUS Server: $($_.Exception.Message)"
        break
    }

    # Get all of the Wsus Groups, and check that the specified source and destination groups exist
    $Groups = $WsusServer.GetComputerTargetGroups()
    If ($Groups.Name -notcontains $SourceGroupName -or $Groups.Name -notcontains $TargetGroupName)
    {
        Write-Error "Source or Destination group names cannot be found in the list of groups on the WSUS Server. Group names are case sensitive. Please check your names."
        break
    }
    $SourceGroupObj = $Groups | Where {$_.Name -eq $SourceGroupName}
    $TargetGroupObj = $Groups | Where {$_.Name -eq $TargetGroupName}

    # Get all of the updates on the server
    Write-Progress -Activity "Getting Details of all updates"
    $Updates = $WsusServer.GetUpdates()
    
    # Go through each of the updates. If the update has an approval for the source group, then create an approval for the destination group. 
    $i = 0
    $Approved = 0
    ForEach ($Update in $Updates)
    {
        $i ++
        Write-Progress -Activity "Copying update approvals" -PercentComplete (($i/$($Updates.Count))*100) -Status "$i of $($Updates.Count)"
        
        if ($Update.GetUpdateApprovals($SourceGroupObj).Count -ne 0 -and $Update.GetUpdateApprovals($TargetGroupObj).Count -eq 0)
        {
            Write-Host ("Approving {0} for {1}" -f $Update.Title, $TargetGroupObj.Name)
            $Update.Approve('Install',$TargetGroupObj) | Out-Null
            $Approved ++
        }
    }
    Write-Progress -Activity "Copying update approvals" -Completed

   Write-Output ("Approved {0} updates for target group {1}" -f $Approved, $TargetGroupName)
}