If your Belgian PPL is an ICAO PPL, then the conversion does not require you to do all the instruction hours all over again. But if it's restricted to Belgian airspace I suspect it's not an ICAO PPL somehow. After all, an ICAO PPL would allow you to fly worldwide. So I guess we're going to need a few more details on the exact license you have, and where the restriction comes from.
If it's the equivalent of, say, the UK NPPL, the Dutch RPL or the FAA Sports Pilot License then the conversion may not be as straightforward as the conversion from an ICAO PPL.