Updating a list item using Powershell is a very common task in the Sharepoint world. An article has been already written about how to create a PWS script which connect to a Sharepoint List and get’n’update the List items in it.
There is ModerationInformation.Status property for these items if the approve process is enabled on the list. You can change it as below:
$item.ModerationInformation.Status = "Approved" $itemp.update()
Have fun 🙂