Can I link an invoice to a Case ID?

I'd like to create an invoice and link it to a Case ID number. I've created a custom invoice field with the lookup type but I can only get the case account name or subject to insert.

Workflow....

Customer calls with an issue and a case is created
Service guy visits customer and resolves case
Creates an invoice and links it to Case ID VIA lookup field so a full history can be viewed on case from invoice

Appreciate any help