What the Tribunal will do is determine whether the ex-wife’s first marriage was valid, or not. If it was, then your fiance is “off the hook” so to speak - he could not have had a valid marriage with her, and therefore is free to marry you.
However, if it is determined that the ex-wife’s first marriage was not valid, then she was free to marry him, and it is possible that his marriage to her was valid.
They will then investigate that marriage, to see whether it was valid or not. If it was valid, then he is not free to marry you.
If it was not valid, they will look into the reasons for that, and this is what will determine whether or not he is free to marry you, since if he was incapable of contracting marriage in the first instance, they will want to make sure that, in the meantime, he has become capable of contracting marriage; otherwise, they will recommend to him to remain single until such time as he overcomes whatever problem there may be.