It is possible to copy your line items from one table to another through a number of different methods.
You'd isolate the Quote line items in a foudn set by performing a find or using Go To Related record, then loop through them creating records in the other table while passing the info in variables, global fields or a script parameter.
However, it might be that you could avoid the issue completely. With many business, the line items for a quote and an invoice can be identical or nearly so in format if not in content. THus your quotes and invoices might be linked to a single line items table.
With some business, you might even treat quotes and invoices as the same record.
When a quote is requested, you start a record where a field in the record is labeled "quote", when the order is placed, you change the field to "Invoice" and update the appropriate fields to make your quote into an invoice. You'll have to examine your business model and see if any of those options make sense for you or not.