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Since Unleashed will not be handling the payments themselves (we are an inventory management system after all!), this will come down to how the system you bring the orders from manages that :)
As it seems they use an online store to manage the orders, these will then be exported to Unleashed for your stock to be managed there. You can then customise what will be the trigger for that export to happen, and what information is stored there before that happens.
I hope this is helpful! In a nutshell, even though you have the ability to issue invoices and such from inside of Unleashed, the actual payment and its management will happen in your financial software. Let us know if there is anything else we can assist you with.