After being incarcerated for 13 years and all my appeals being denied, but I was offered 15 years three times, can I get that offer back?

After being sentenced, there is no procedure for getting a sentence reduced or changed to the 15-year offer that was made prior to going to trial.  Although the state often engages in what is referred to as "plea bargaining" (i.e., making an offer to try to get a case to settle via a plea rather than going to trial), the state never is required to make any offers.  So even if your brother's case were to be reversed (which is unlikely if, as you indicated, all appeals have been exhausted and denied) and sent back to court for futher hearings, the state would not have to make any offer.  If you find some way to get the case reversed or sent back to the trial court (e.g., newly discovered evidence that could not have been discovered previously -  or -- ineffective assistance of counsel that was not previously known), the state still is under no obligation to make an offer.  The chances at this point of finding some legally-sufficient reason to get the case sent back to the trial court are very unlikely.   Be aware that if, despite overwhelming odds, your brother comes up with newly discovered evidence or ineffective assistance of counsel that could have not been discovered previously, he could file a motion for post-conviction relief.  (If he is in prison for a life sentence, it is likely that he already has tried filing at least one, if not more, post-conviction relief motions.)  Post-conviction relief motions must be filed within two years after grounds for the motion exist.  (Or within two years after the defendant, through the exercise of due diligence, should have been aware of the grounds for such a motion.)  So even if your brother just learned of some new grounds, if the court decides that the grounds existed four years ago and that your brother should have been aware of them at least two years ago, your brother will loose the right to file the motion on those grounds.