By using the module "mailalerts" of Prestashop you will be able to send out Trustpilot's invitations with the Automatic Feedback Service. Read more about the AFS here. 

1- Find your Trustpilot's email address from the B2B > Get reviews > Invitation methods > Trustpilot Automatic Invitations (AFS); & activate the email's notifications for every new order with Mailalerts.

2- Go to Module > Mailalerts > mailalerts.php > Mail > new_order.html

3- Add the following script in the body in order to pass on the customer's information:

<script type="application/json+trustpilot">
{
"recipientEmail": "{email}",
"recipientName": "{firstname}",
"referenceId": "{order_name}"
}
</script>

{order_id} = order number (12345)
{order_name} = reference number (ABCDE)

4- If you also want to collect Product Reviews, you will at least need to add the following information to the script: 

<script type="application/json+trustpilot">
{
"recipientEmail": "{email}",
"recipientName": "{firstname}",
"referenceId": "{order_name}",
"products" : [
{
"productUrl": "{mUrlu}",
"name": "{nomProduitu}",
"sku": "{SKUu}"
}
]
}
</script>

Follow this guide if you want to use other structured data snippets to personalize even more your invitations (ex: send invitation in different languages, add a picture to your product review invitations...): Add a structured data snippet for Automatic Feedback Service

4. From the email settings, select which template you want to send to your customers & add if needed an invitation delay. 

Now every time a new order is confirmed a Trustpilot's invitation will be created. You can see it from your Invitation history.