A written account of the particulars of merchandise shipped or sent to a purchaser, consignee, factor, etc., with the value or prices and charges annexed.(noun)
source: webster1913
verb (v)
send an bill to(verb.possession)
Example: She invoiced the company for her expenses.
source: wordnet30
To make a written list or account of, as goods to be sent to a consignee; to insert in a priced list; to write or enter in an invoice.(verb)