If you have Use VAT Calculation Service enabled, there are extra options to make the management of VAT invoices more convenient for you.
In case you want M2E Pro to keep creating standard Magento Invoices, you can enable Magento Invoice Creation option:
VAT invoices will be uploaded automatically to Amazon, while Magento standard invoices will be kept in your Magento.
An important step is to fill in Store Name and Store Contact Address under System > Configuration > General > General > Store Information.
This information is vital for the correct generation of VAT Invoices.
Additionally, there is an option to upload a custom logo to the printed version of VAT Invoices. To do it, go to System > Configuration > Sales > Invoice and Packing Slip Design.