So true, we're facing the same problem since June 2019.
I came on here to see if there are any solutions that might have come in the recent past, but everything looks exactly the way it did over a year ago.
I'm using a few apps from MLVeda to make multi currency checkout work with paypal. I would have preferred a more robust solution from shopify, but this is close enough for the time being.
I willing to have only Paypal on my website, but even that doesn't work, it's ridiculous because paypal works effortlessly with a few other online store platforms.
No problems at all.
We use their currency converter, which "talks" to their checkout app. We loose the ability to customize the checkout page with our colors, but atleast the payments work.
They also recommended an invoicing app called invoice hero, this app auto creates an invoice in the currency the customer used to pay.
You can reach out to their support, they typically respond within 24 hours.
This topic is from January 2020 and now we are in 2021. Im facing the same issue with PayPal express in combination with Shopify Payments. Customers are mailing and complaining about this since their orders and invoices are all in the wrong currency. Despite selecting the right currency on the site. Also due to the conversion rates by PayPal the transaction price doesn’t match with the order price on the checkout page, which is totally unacceptable for any business and customer.
Shopify : apparently this issue is now there for over 1-2 years! Please take action on this. This is absolutely a showstopper defect for many.