Work related ESA and full time studying.

Hi. My son (38) has been on work related ESA for about 3 years now. (He suffers with depression) He also receives carers allowance for helping me, as I am disabled. He lives at home with me.
He wants to enrol on a full time course in our local college to train to become an electrician. He was so excited to think that he could be getting a qualification. Now the DWP have told him he'd have to sign off ESA if he starts a full time course. Someone told him that if he gets a letter from his GP saying that this course would benefit his health / mental state, then the DWP might allow him to keep his ESA. He doesn't know what to do now. He so wants to get on this course, but financially he can't afford to loose his ESA.
This is an URGENT enquiry, as he has to make his choice within the next few days. I'd be extreemly grateful for any advice.