Hello Geoffrey - I am sorry to red of your loss.
If the property is in joint names then form DJP plus a certified copy of either the death certificate/probate can be used to update the register re the death.
Form AS1 is only used if the whole of the legal title is being transferred from a sole deceased owner to their beneficiary. That can't happen here as the legal ownership passes to the surviving joint owner.
If the legal ownership is to be transferred to include the deceased's beneficiary then you would need the surviving owner to transfer the whole of the title to themselves plus the beneficiary as appropriate
You can use our online assisted guidance to find answers and links to the forms/guidance needed depending on what updates are required -
HMLR Guide: Start - External · HM Land Registry