Not sure what to do, Mum Passed away

Hi, i am on new style esa contribution based, no income based element in the support group. My Mum died of cancer last month and i am her oldest child so having to sort out all her finances. Her private pension, life insurance and bank account will be paid in to my bank account, a total of around £4500 in all. The pension have asked for a full bank statement with all transactions unredacted, so im worried they will inform dwp when they see i am on benefits, its for an amount of around £550. My questions are, firstly, would the pension company contact dwp? and secondly, should i do so anyway to let them know why there is money being paid in or does it not matter as im cont. based? Im under an enormous amount of stress, grieving, and my depression and anxiety are through the roof and i cant think straight, so any help would be really appreciated. Thank you