You are responsible for proving that you lived with your late partner. Here are some examples of what evidence the Department for Work and Pensions (DWP) will accept as proof of address/cohabitation:
Local Authority council tax statement
United Kingdom (UK) full or provisional photo-card driving licence
Correspondence from HM Revenue and Customs , for example most recent tax notification
tax assessment
Statement of account, or notice of coding
Mortgage statement from a recognised lender
Local Council rent card or tenancy agreement
Confirmation from the electoral register that a person of that name lives at the claimed address
The DWP will accept photocopies of these documents.