Hi Martinr6899,
If goods are exported to Italy then the supply should be zero rated as long as the conditions are met below:
Conditions and time limits for zero rating
The import VAT in Italy would normally be paid by the importer of the goods in to Italy.
However, if you are the importer of record for the goods in to Italy then it would be your responsibility to account for the VAT in Italy and also the VAT on the sale of the goods in Italy to your customer.
Thank you.