Yes that is possible by doing some studio customisation. You flow is like below,

Invoice Lines > Sales Order Lines > Stock Move > Stock Move Lines > Lot/Serial Numbers

Here video you can see => https://www.youtube.com/watch?v=2fu13bWCqEM

Hello,

You can add "Internal Reference" as a serial number in product and it will display in every product. But for invoice you need to customise that feature to do this.

Thank you.