ESA Query re Mums Death

Hi, My Mum died of cancer 5 weeks ago and as her eldest i am having to deal with her finances. Im on esa new style in support group, contribution based, no income related element. I stand to inherit about £2000 in total, but all of her money from her bank account, private pension and life insurance, which will be in total around £8000, will be paid in to my bank, i will then divide it equally between myself and my 3 siblings as per my mums wish. My anxiety and depression are through the roof, i cant stop crying and i cant think straight, so i have 2 questions please, firstly, the pension asked for full bank accounts without the transactions redacted, so they will see i am on esa, are they looking for this and is this why they wanted the statement? Are they likely to call dwp? , and secondly, should i call them anyway and inform them where the money is coming from? could i be in trouble if i dont? Im worried sick so if you could advise i would be grateful.