How to handle subscriptions for people outside Shopify Platform

Hello team ,

We are developing a shopify app for first time and we would like to have few things clarified

We have a software that can be used outside shopify platform

How to handle subscriptions if people buy the tool annually directly from our site , uses it on non-shopify website and then later add shopify integration .

Since , the merchant has already purchased the tool from outside,

how we should able to handle subscriptions from next billing cycle ? should we bill from the original source of payment or we need to migrate the billing to shopify billing API

Any tip would be helpful . Thanks in Advance