If you know the FI document number of an Invoice in SAP system, you have at least two methods to find invoice number from FI document number.
The first method is using the VF03 tcode. When you call the transaction code VF03, you can use the More Search Criteria filter section to use the FI document number for finding invoice number.
For example, in the below VF03 screenshot supply the FI document number, company code and fiscal year. When you press Search button a list of SAP invoice documents will be listed in the popup screen as seen in the sample. Click on searched invoice row, this will carry the reference key column calue to the billing document number textbox to display the SAP invoice document.
The second method to find invoice number using FI document number is using FB03 transaction code. In fact this screen is same as the previous search screen.
Only the result screen is different than the previous list. But tcode FB03 can be used with same search parameters to find the SAP invoice number easily.