If you have access to Ancestry, go to the card catalogue and search for
England & Scotland, Select Cemetery Registers, 1800-2016
put in his name and year of death, Liverpool as the place and he comes up as first on the list of results.
If you don't have a sub, your local library may well have access to Ancestry from the pcs in the library.
As its a public grave, its doubtful that there will be a headstone and other family members are not likely to be interred in the same plot.
Boo