I recently had a not-very-expected bereavement.
I'm not sure how far along the family are will the process, but the admin was absolutely daunting, so I'll go from the beginning.
While I could hardly think, the widower couldn't think at all. The first problem was getting the death registered. There are all sorts of dire warnings about having to register it within 5 days. That turned out to be nonsense and a lot of people can't get the Certificate of Cause of Death from the doctor for weeks. For peace of mind we called the Registrar and then we knew they had been told. It's best to use the Registrar for the area where the death actually occured, even if that's different from the deceased's home. It's not essential, but it makes things easier. They may even have a form on their website to make the first contact, which you could offer to help fill out. The next thing is to get lots of Death Certificates - several people request originals and they're cheaper and easier to get at the time. 6-10 I would say, depending on the deceased's financial arrangements.
They would normally need to find a funeral parlour. IMO it's worth paying for them to sort things out at a time when decisions are hard. They can guide you and make suggestions to chew over. If the family haven't found one, if you can see if anyone locally can recommend one that would help. or offer to call around for somewhere you think they'll like. Does anyone want to see the deceased in his coffin?
If there's to be a funeral or cremation service a 'celebrant' (I don't think they're called that!) will need to be found. The funeral parlour can help. If the family are connected to a church, that can be very useful as the Vicar can guide and suggest. If you knew his taste in music or hymns (if appropriate) you could make suggestions. It's usual to write a eulogy - I couldn't think how to begin, but the widower wanted to do it. It's a good idea, if no one can bear it, to ask the celebrant to read the eulogy and any readings. They're usually OK if someone wants to read at the last minute. IME there is absolutely no way you can know how many people will come, so if organising a Wake, it's a good idea to use a place that can whistle up extra tea and cake at a moment's notice (pub, sports club, etc), and book for a smallish number first. We just ordered 100 Orders of Service, not minding if people had to share, or we had too many - the differential cost wasn't much.
The 'Tell us once' service actually works. You could offer to sit with them while they fill that out - they will need all sorts of numbers like his National Insurance, NHS, etc. There are various similar for non-government organisations, but nothing covers everything like the Government one does for all the State stuff. His employer or pension provider will need to be informed and any provision for his widow sorted out.
The finances may, or may not, be a nightmare. Any accounts in both names are fine; the balance goes to the survivor. Anything in just his name will be frozen. Someone needs to contact each organisation and inform them. Some are considerably more helpful than others, so if there several accounts with different organisations, a trusted friend making the original calls to the relevant bereavement department can be a help. The wife would have to be on hand to confirm that it's OK for them to speak to said friend, or possibly take over, but making the first contact can seem like a mighty hurdle. Even going through his affairs and making a list of organisations, account numbers and phone numbers can help. For small balances funds may be released to whoever is entitled to them quite quickly, possibly within days. For larger sums, generally over £20,000, depending a bit on each organisation, probate will be required. The first step here is to get a closing balance sent. And usually send a Death Certificate.
If there is a Will things will be much easier as if everything is left to the wife there is no inheritance tax to pay. But probate will still be needed for large sums. Who is the Executor? It can all be thrown at a solicitor to deal with, but that's not cheap. Would help to find a good/recommended solicitor help?
The main thing is to help them understand that there is absolutely nothing wrong with being mentally frozen. They haven't fallen apart because they can't make the slightest decision - it's a normal human reaction. Regular invitations to have a coffee, and get out of the house, then offers to help with some of the above, could, I would think, be welcome, even if you are refused over and over again. I think, just keep hovering in the background and take no offence if they don't want your help. Let them know the door is never closed.
Later, be prepared to let them say the same thing over and over again. You may feel you are not helping because they don't seem to move on. Just listening when they can't get past it is a help. It's common to feel you mustn't keep moaning to people. Let your friend know she can moan to you as much as she wants.