That is a ground wire that runs back to the VR attaching bolt to the firewall
OPs dad was way ahead of all of us!
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When you bought your new alternator what year did you specify?
Assuming the alternator was the only thing wrong with the charging system with the brown wire and the green wire attached to the ALT it should charge. Adding the dedicated ground on the ALT is not an issue.
if it is still not charging measure the voltage on the green wire to ground while the engine is running 6-8 V would be normal.