No, he cannot: a person who is legally incompetent to handle his own affairs may not, as you correctly point out, exercise a power of attorney (whether a standard one or a medical one) for someone else. Your mother needs to appoint someone else to this role. Incomptetent is incompetent: once found to be legally incompetent, you  are  legally incompetent in all spheres of your life, for all exercises of legal authority.