G-merl is a new and separate robot based on the data Eggman had on Emerl from his research. He's his own bot. With that said, at the end of Sonic Battle, Sonic and Cream makes a small speech about how Emerl will still be with them in the Emeralds. After they find G-merl washed up on the shore and Tails fixes him up and removes his weapons, they notice how he is peaceful and not attacking anyone. Its nothing directly stated, but that's always how I interpreted it as what remained of the original Emerl's "soul" was inherited into him after the Ultimate G-merl incident through the Chaos Emeralds. Given the whole lesson at the end of Battle was how the world would only know peace once we didn't need weapons, I think it is meant to be poetic in that way. So I would think of it as him having been "reincarnated" if you will, assuming this is very much the intention they had with the writing here.