Avoid paying tax using layers

[elmarna]

Hello, to avoid paying taxes, I would like to set up an account with a foreign payment gateway that can also send invoices. This way, when the customer make a payment to the payment gateway, the money will be transferred to a foreign bank account. However, I have a couple of simple questions:
Can the VAT be registered as unpaid on my end since the person I am collecting the VAT from can reclaim it through the tax system?
Which payment gateway would you recommend, Stripe, Braintree, or another?
Please provide some input.