Problems in local government entities, about the change of Coordinate System from psad56 to wgs84

Even though there are many professionals with knowledge of cartography and geodesy, in the local government entities in Peru it is still difficult for those who work within these, to generate a reference or map in which it is reflected, the real change or conversion of the psad56 coordinate system to the wgs84 system without this causing numerical location problems.
It seems that there is no complete training on the part of the entity or self-training on the part of the professional, that is why these errors, and also the fact that many have delegated the validation of the topographic and geodesic information to the technical assistance personnel.