WooCommerce Send Cart to Checkout on 2nd Website

I have website A running WooCommerce that needs to send the cart details to website B for payment. Website B will store all the order details for website A and process any recurring payments as normal with WooCommerce.

I need someone to quote for creating this functionality in my existing website.

Specifically, website A is a photography website but the type of photography is risqué, so my clients do not want it to show on their credit/debit card when they book on my website. The only way to achieve this is to direct the customer to complete the payment on website B, which is a different name and hence the card statement descriptor will be different and not directly linked back to website A.

Ideally they will be automatically directed to website B when they hit the checkout button. User accounts are to be synced between website A and website B.

After the purchase has been completed they can then be redirected back to website A to continue browsing.

All orders to be maintained on website B for normal billing purposes.

Website A is set up on WordPress multisite, website B is part of the multisite of website A.

I basically need a plugin created to send the cart from website A to the checkout on website B.