Yes the balancer and convertor/flywheel on any motor are either neutral balance for internal balance motors or are both have to be externally weighted for external. So yes you need a external balance convertor (weighted) and external balancer.

Two other things to think about
1. Someone has internally balanced motor thats why it has internal balance balancer/convertor but then you wouldn't have any vibration.

2. It was rebuilt without concern to balancing the components and no balancer or convertor will put the vibration to rest without taking motor down and taking rotating assembly to machinist to balance.