RAB is the name of one of the founders of Borgin and Burkes, Mr. Burke. He snuck onto the Hogwarts grounds following the murder of Dumbledore, and using either the general confusion or an invisibility cloak (as the owner of a shop he would have invisibility cloaks available to him) as a shield against being seen. He went through the corridor created by the closets--which was never closed--and escaped in the same way.
He went to Dumbledore's body and took the Horcrux, replacing it with the fake locket.
Plausability factor is high. It is more likely that one wizard was able to come through the closets than to steal the locket from the cave. Also, the cave did not bear the signs of having been broken into before Harry and Dumbledore went there. Most importantly, the potion was still there, and it was not self-filling.
RAB said in his note that he would be dead before the note was read. This is because destroying a horcrux is very damaging to the person who destroys it. Remember that Dumbledore was nearly killed, and permanently damaged, by destroying a horcrux at the beginning.