Your new regulator has a stuck cutout relay. Take the cover off the regulator and look at the contacts behind the Bat. terminal. They should be open. If they're stuck closed the battery will discharge itself through the generator. This usually ruins the regulator, and sometimes the generator as well. I'll bet nobody checked the regulator for proper adjustment after it was installed. On a 12 volt system the cutout relay should close as the armature voltage goes above 12.5 volts. It should open anytime the generator voltage goes below battery voltage. Some cutout relays stick or fail to open at the proper time as the engine is shut down, even on a brand new "Made in China" regulator!
Jerry

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