This is Max from the Shopify Team.
Short answer, no. There wouldn't be a way to process a refund within Shopify for an order that took place outside of our platform and the connected payment processor. You must offer a refund externally for orders placed elsewhere. You could, however, record this order and refunded amount within Shopify.
If you are wanting to move old order data from one platform over to Shopify you could do this in a few different ways. App integrations can help import information over for your client's records quickly! Check out a few options here. Keep in mind that some of these can be costly, so, if this is only important for one order, you might want to consider other options.
Draft orders are another option for recording details. This might be a quick way to create and reference a customer and their order details within the new platform. Check out some of the details on that process, here.
Order notes and tags are a great tool for adding greater context and search-ability to your orders (this could be for imported orders, drafts, new orders). I'd suggest adding one or more of these options to your imported orders for some clarity!
Let us know if this helps you get prepared for your client's new shop! We also have some great resources to share, like this Help Doc: Migrating to Shopify from another platform, that might come in handy as you explore the platform.
If you have any more questions about re-platforming, feel free to let us know here or reach out to Support directly here.