Daisy, I am sincerely sorry for your loss.
Probably the best help you can give your mum right now is being with her as often as you can.
I think a lot of us, when one parent dies feel we "have to" take over and do everything. This is rarely the case.
When my mother died, my father greatly appreciated that my sister and I carefully made a point of asking HIM what he wanted done and when. He was still in full command of his mental faculties but not so able to sort through papers, clothes etc.
It is important to remember that our bereaved parent has lost his or her husband or wife. This is a very different thing to loosing a parent - believe me, I have been bereaved of both parents, my sister and more lately my husband.
Loosing a parent is hard, very hard, I am not saying it isn't.
But you need time and space to deal with the loss of your father, so please, do not do things you mum can and should console herself by doing.
Work with her as a team, and remember that she knew your dad before you did.