Can you identify this bike of my mothers from 1960?

Well all of her bikes were British bikes up until she started riding Vespas later in life. She started out on her boyfriends bike when she was 15 in 1959 and then kept riding all her life until her health would permit it no longer. She was still riding a motorcycle to work up to the 8th month of being pregnant with me, stopping every morning at the same bus stop full of people to throw up each morning.

Somewhere I have a list of all the bikes she had, but cannot locate it at the moment. They included BSA Bantams, Triumphs, and two of a name I had never heard before, something like Morgans or Martins.

This picture is dated 1960, Location would be in or around Southampton England, and perhaps was her first or second bike?

yes ,I agree ,it certainly looks like a Francis Barnet cruiser, I had one

In 1957, the Cruiser 80 was introduced.
Francis-Barnett was forced to fit the new 249cc AMC single cylinder engine into the Cruiser 80, however these engines proved to be problematic and AMC even sent some of their own engines to Villiers for modification.
AMC reverted to using the trustworthy Villiers twin cylinder engines in later Cruiser 80s.

In 1959 the Falcon 87 was introduced. This was powered by a 199cc single cylinder two stroke AMC engine. Production of the Falcon continued until 1966.


Also, in 1959, came the Cruiser 84. This featured a fully enclosed rear wheel and leg shields as standard equipment.
With AMC themselves in financial trouble, Francis-Barnett production was transferred from Coventry to the James factory at Greet in 1962 in order to cut down costs.
The James company had been taken over by AMC in 1951.