It doesn't help searching when the FS catalogue has the area down as 'Sephton' rather than Sefton :-)
I do think the record is in the 'quite likely category' but agree that confirmation of the address at the time of death would be good.
The cremation number and the date of death, would, I'd guess, make it easier for them to check.
Not sure what info they normally give out, but if Registrars are anything to go by then given the name, cremation number and d.o.d. and a query asking if this lady's address at the time of her death was xxx would enable them to confirm or deny.
Fingers crossed you get the confirmation you need.
Boo