"This is not his brown suit."
Translation:Це не його коричневий костюм.
No, that sounds wrong. If you said "Цей коричневий костюм не його", that would work, but it would be a different sentence ("This brown suit is not his").
Це is the subject of the sentence which is saying "Це ≠ його коричневий костюм". Shuffling the words like that makes it ungrammatical.