And when was the time in history the auto-pilot became functional for the first time?

Nope even earlier than that.
Sperry produced a prototype in 1912.
The Curtiss Condor was licensed to operate with an autopilot in 1931.

http://youtube.com/watch?v=lBBp8hfPlOs

In WW2, the autopilot was nicknamed ''George'' from a movie (or advertising campaign l am not sure which) line ''Let George do it''. Which meant it is someone else is problem.

Wow, Jim has a good answer. l was going to say that auto pilot were introduce to commercial airlines in the late 70 is after U.S. plane have fully developed the system

Nyanna:

The first autopilot in 1914, Charles Lindbergh’s first successful solo flight across the Atlantic in 1927, Amelia Earhart’s landmark flight in 1932, and the world’s first sonic boom in 1947, were all made possible because of aviation technology developed by Honeywell and its legacy companies,

Source of data, Honeywell.

Mind Doctor, Panama

Good question and after forty years flying I've not a clue.

l suppose when the wright brothers invented the first plane,

Jimbo is correct

Curtiss Condor - 1931
Subsequent to the above, auto-pilot came into being.