It will cost you as much to 'convert' a non JAA licence as it would to get a JAA licence in the first place (provided you shop around for your training). If you spend money getting a SA licence with the intention only of using it as a stepping stone to a JAA licence, you will be throwing your money away. The same applies to any non-JAA state licence - they are worthless within the JAA.
If you want to fly in the JAA, consider only schools that are JAA approved. Bear in mind, however, that a licence gained as a result of training at any school outside of the JAA (e.g. SA, USA) will not have been gained in accordance with JAR-FCL and there are JAA states (e.g. France) which will not recognise it.