There are a few points to be aware of when discussing the checkout currency for a given store.
The currency in which a store’s customers can check out would be determined by the payment gateway being used by that store.
If you can confirm in which country this store would be based, I can share a list with you of all payment gateway options available there.
Should your requirement specifically be that you just wish to issue an invoice in a given currency (rather than having a customer check out in that currency) then you could look at other ways to handle this such as using an invoice app like Sufio.
Let me know where the store is based so we can share your options in terms of payment gateways and let me know as much as you can about invoicing your customers and what you’d like to be able to do in that regard.
As these are all third-party, non-Shopify gateway options you’d just need to consult whichever gateway provider you’re considering using to confirm their functionality in terms of currency and invoicing.
If you’re happy to separately send an invoice to your customer separately from the automated order confirmation email, you may be able to do so using an invoice app from our app store.
As with all third-party apps in our store, you can reach out to the developers directly with any support queries you have by using the contact details listed there on the app store page.
Let me know if there’s anything else you’re working on for the Shopify side of things so we can help out!