Let me tell you straight off the bat that English words do not usually end in “u,” and when I saw this spelling of through (thru) for the first time, I was quite literally disgusted at such an abuse of the English language.
However, the spelling thru has an entry in the very tolerant Merriam-Webster that leads to through. On the other hand, the more sensible OED has no entry for thru, although the spelling is listed alongside other historical variations of the word through.
In recent years, Thru has established itself as a modern spelling of through, and is often associated with the online world where the term “click thru” – a click through to a website – is preferred to “click through.” It has, however, resisted the efforts of various organizations such as newspapers and people in high places to get it accepted for general usage. And with that it mind you shouldn’t use it in professional writing.
There is a history of trying to get this variation of through accepted, and The Chicago Tribune started using thru in 1934, but finally gave up in 1975 and went back to through. Through was also on reform lists issued by the National Education Association in 1898, and the Simplified Spelling Board in 1906. But it never did make it thru for reform.
With the evolving “SMS language” creeping into everyday usage it is quite feasible that variations of words such as thru may be accepted into all areas of everyday writing in the next 10 or so years. But for now, where professional writing matters are concerned, you should use through.