Synonyms for "The most important thing for them to successful is their union. "

A synonym is a word or short phrase that means roughly the same thing as another word or short phrase. Your sentence doesn't make sense.  It seems to be an incomplete thought.  There is no synonym for it.

I agree with Patty that there is no synonym for a sentence. However, I can correct the first part of your sentence.  It should be The most important thing for them to be successful...  Perhaps the rest of your sentence needs to be changed to an infinitive phrase?  This is only a guess.

The most important thing for them to be successful is to be united.
 

If I have gleaned your meaning correctly, the above sentence is still not quite correct. (At least it doesn't sound correct to my ears at 11 pm on a Saturday night.) Being united is the most important thing for their success or Their success depends most upon being united sounds better and either is grammatically correct.