I thought at one point there was a thread on this.
Regardless, I would think that he would have been sent through the door with the other Telmarines with Pruniprismia. I don't think either Pruniprismia or her son would have been allowed to stay once Caspian was on the throne. They wouldn't have been good at being subject to him and anyone with that attitude was sent away. I think Aslan would have made sure that was the case since he said that Caspian's line would rule from then on. This would be much easier without anyone else in Narnia who could make a claim to the throne in any way. Just my thoughts.