Is it possible to turn a pro-forma invoice into a VAT invoice?

Yes. It is possible to create a VAT invoice on the basis of a pro-forma invoice automatically.
Select the item you are interested in with the pro-forma invoice (list of documents window
Invoices -> Invoices -> List of documents) and click on the menu of additional options (or the right mouse button)
by selecting pro-forma invoice -> Faktura VAT.