If multicurrency is enable in your QuickBooks account, you can set the currency for the customer when you first create the customer.

However, QuickBooks does not allow you to change the currency for the customer once created. In the below image, you will see the currency is greyed-out and you are not allowed to change it.

Thus, the currency for the invoice is locked to the set currency of the customer and it is not possible to change the currency for a specific invoice.

If you want to have a different currency for your invoice, you will need to create a second unique customer for that currency.

In the below image, we have two customers (flag icons added manually):