1
general::
Say or write and send away rapidly, as in He fired off three more questions, or She fired off a letter of complaint to the president. This expression originally (from about 1700) was, and still is, used in the sense of "discharge a weapon or ammunition," as in The police were instructed to fire off canisters of tear gas. The figurative use dates from the late 1800s.
American Heritage Idioms
2
general::
Phrase(s): fire something off (to someone)
Fig. to send something to someone immediately, by a very rapid means. • Fire a letter off to Fred, ordering him to return home at once. • I fired off a letter to Fred as you asked. • I finished the email and fired it off.
McGrawhill's American Idioms And Phrasal Verbs