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If you're sure that the alternator isn't charging the battery ( does the battery voltage increase after engine start?) I'd start by tracing the small diameter wire back from the alternator
as the alternator is switched over to charging by the engine ECU and if the wire is broken or has a poor connection then you'll have issues
if the continuity between this small wire connection and the ECU socket is OK then its possibly the ECU is at fault and it can be sent off for repair
I don't quite understand
you're measuring voltage at the cigarette lighter and with the engine off its at 11.5V and when the engine is started it rises to 14V?
if so then the alternator is working fine
so the battery isn't being charged then:
either the new alternator is faulty
the 'sense' or switching wire on the alternator is somehow broken so the signal isn't getting back to the ECU
The ECU is faulty
I'd start by tracing the alternator wiring back as the next step