Balanced 360 Motor w/4-speed?

Check to see if his converter just has the factory weights on it, or if there was any other non factory balance weight added or removed. If it just has the factory weights you should be fine with the correct flywheel for the LA 360 ( I am assuming it is not a magnum 360). Is this a street car or a race car? What rpms do you plan on spinning?

There is a less expensive way to do the flywheel if you already own a neutrally balanced one.