If the alternator takes a different connector then I can assure you the regulator is the issue. I found that no matter what I tried the computer on the h3 would not recognize the alternator until I had a local shop put the right regulator in it. Like I said earlier the 3 expects a specific regulator and won’t see anything else. This is the regulator that came in new alternator. Replacing the plug end won’t help even though the wires are the same.
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This is stock. If you take the 240 to a alternator shop and ask them to verify the regulator will work for your application they can show you online where the internal signal components are different for the H3 regulator. Parts and labor to switch regulators was about $75 for me.
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Your situation sounds identical to mine. I was upgrading getting ready for dual battery, lights and winch. Put in old and all was good. Put in new with different connector and charge was minimal at best. Now with right regulator everything is good.
looking on eBay you can get the right regulator for $36 or so if you are comfortable changing yourself.