Using Classic Outlook on Windows for personal email, calendar, and contact management
I am sorry for your loss, if you know the password to their Microsoft account, you can close the account using the steps provided on this link, that process will also close their Outlook/Hotmail account.
https://support.microsoft.com/en-us/accounts-billing/manage/how-to-close-your-microsoft-account
If you do not know their password, then because Microsoft take account security very seriously, on the link below is the information they provide to access someone's account after they have passed, it is basically a legal process that needs to be entered into to access their account.