The first thing you should do is to make a formal complaint to whoever was in charge of his care. The charge nurse on the ward where he was nursed should be able (and willing) to give you information about their complaints procedure. If you are unhappy with their explanations as to what happened to your Mum's partner, you might then consider consulting a solicitor, but speak to the hospital first. Don't involve yourself with the expense of a solicitor until you are sure that you want to take action. I know you are probably feeling quite angry and upset now, but if you are given full explanations and/or an apology for what went on, perhaps you might change your mind.
Suing the NHS is a very long, frustrating, time-consuming and expensive process. They have huge resources available to them to fight off actions brought against them , whereas you have only your own resources.
I am sorry for you and your Mum but please think long and hard before embarking on this.