THe identity of Mary Stringer is fairly certain.
The only suitable baptism Mary that has been found gives her parents as Peter and Martha.
They were living in Fakenham too and had several others children born around that time.
Their marriage is the only suitable one for Peter and Martha in Norfolk and this too was at Fakenham.

Searched FREEREG for baptism of Peter Stringer in Norfolk 1720-1745, two fond in West Rayham, but both appear to have died in infancy.

Searched FREEREG for burial of Peter Stringer, although one found for Martha which mentions him, no Burial found.  Wighton registers also consulted.
On the face of it he was still alive when Martha died in 1822.