President Theodore Roosevelt (1901–1909) promoted a spelling reform that include "thru" for "through," "tho" for "though," "altho" for "although," etc. It did not catch on. "Thru" is not a standard American spelling of "through"; unlike words like programme/program and mediæval/medieval, the spelling of "through" is the same in American English as in non-American English.
Although "through" is sometimes abbreviated "thru" for commercial and advertising effects, including as a prefix (as in the limited access highway in New York State called the "Thruway"), I don't think I've seen "thruout," probably because of the bizarre vowel cluster that it would have.
I agree with the others. I just wanted to add that "throughout" is a fairly formal word in itself. Someone going for economy of words and casual speech/text would probably choose another word, in my experience.