VERIFIED SOLUTION i
The current behaviour in MapInfo Pro v15.2 is that in order to copy across BOTH map object and attribute data from TableA to TableB, users will need to copy and paste the actual map object in the map window e.g. select the object in TableA, press CTRL+C, then make TableB editable in the Layer Control and with the map window active, press CTRL+V. If you copy and paste the table attributes only from TableA to TableB, the map objects are NOT included in this operation.
UPDATED: March 28, 2017