I agree that he should use \vec{J}(r,\vartheta,\varphi)=I \frac{1}{a} \delta(\vartheta'-\pi/2) \delta(r'-a)\vec{e}_{\varphi}
where r',\theta',\phi'are spherical coordinates for the current
At risk of repeating what some of you guys have already posted, I'll write the procedure I'd usually...