It's very hard to prove something doesn't exist. You may need to clarify with them what they will actually accept, but I imagine it will need to be something like an 'affidavit of search'. You may need to engage a professional search agent to conduct registry searches in all relevant jurisdictions (i.e. states) in which your mother lived where she owned property (for example).
However, ask them what they require rather than guessing. If you provide something that's not quite what they want you may need to do it all again.