With a registration going back around 50 years it can be difficult to unravel the true history.
There are some options here to be thought about. For example, the car could be a Mk.1 which was exported, then re-imported in 1968 - 9. It would have been given a G-registration as age related plates didn't get allocated back then. I imported a 1973 car from Germany in 1979 and it was given a 1979 registration.
If the car had been badly damaged in 1968 -9 it could have been repaired with a Mk.2 shell. This was not uncommon, although it might have been expected that the rectangular rear lights would have been retained as they were much better than the Mk.1 type.
It could simply have been restored using a later Mk.2 shell, either new or used at the time when re-shelling was acceptable and the Mini was not such a valuable classic. Again, not unusual.
It might be a Mk.2 998 'ringer' made to look like an 'S'.
The A+ engine may have been fitted to replace a worn-out 'S' engine, although this would seriously devalue the car. With full 'S' engines rebuilt and ready to install costing many thousands it is easy to see why this might have been done, but to try to pass it off as a genuine 'S' is a bit naughty - 'caveat emptor!' But then, what could have happened to the original 'S' engine. Does it have an 'S' gearbox one might wonder?
If the log book shows it to be an original Cooper 'S', Mk.1 or Mk.2 it does have a high value, maybe £12,000, as it would not cost too much to make it all original again, although finding a block might be difficult. A 1275 'S' block might cost around £800 and a crank around £500 with rods at about £75 each. So it is 'do-able'.