The current ward clerk will be able to see when the membership record was moved into the ward, but that is not necessarily the date that the member moved in. And he will not be able to see when the record first showed up in the previous ward.
An approximate date can be calculated by looking at old bills or other mail. Another way would be to look through old checking account statements, where the member should be able to see where he stopped paying Georgia Power and Light and began paying Texas Power and Light (or whatever they were called). Bank records are usually kept for seven years.
I have regularly had to be able to furnish a list of addresses where I lived, so I keep a record of all of them.
Being a detective can be fun, but it does take time.