How to run the autoinvoice process from DOO to AR by the SO number and not by the source order?

In Order Management, we are using mostly different integrations to create the sales orders (instead of vanilla SO screen). In this case, the SO number differs from the source order number. This cause an issue in running the autoinvoice process (users are not familiar with the source order, the SO number is what is noticed).
The same issue is in the AR when searching for the transactions - the "Reference" field refers to the source number and not to the SO number.
Is it possible to run the autoinvoice process and then search the invoices in AR using the SO number, and not the source order number?