With loss of both gens,capt will be (become)pilot flying and i hope it is so in all your manuals/sops...
Nope. The only automatic transfer of control in ours is for a rejected takeoff. It might be a prudent option during FORDEC to transfer control, but it is not required by the checklist nor by the SOP. It was different on the classic though. On the NG there is that brightly illuminated ISFD that will work for 1:45, or 45 minutes longer than battery power and is easy to fly from both sides.
To be honest, the loss of both engine driven generator checklist is a behemoth with its six pages and numerous decision points. It is one of the checklist where it is better to use it on the EFB in my opinion as the links make it that much easier to navigate through that thing.