You really need to check whether it’s worth it, because you will be paying capital gains tax on the transfer. This may be more than the reduced tax, especially if his tax is going to increase later on when he goes back to work.
Why not start investing everything in joint names, and (if you are in dividend reinvestment plans) stop any dividend reinvestment into your name?
The mechanics of share transfer are easy, you get the off market transfer form from the share registry of the company whose shares you wish to transfer, fill it out and send it to them.