If JS likes the song that much, surely he'll be happy to pay a fee to perform it, but leave you the correct authorship.

After all, if you sell him the right to claim it as his own, then he'll get any and all residuals and copyright; if it becomes a hit for him and others re-record it and it's a hit for them too, all those profits and all that credit will go to him.

I'd say the little bollocks is chancing his arm.