Is a 2001 outback 3.0 motor work in a 2004 outback
If you put a different wiring harness in and depending on transmission model
Think so, but may get tricky if the '04 is the later CA-New England low emissions (early PZEV) model, as ECM, cats, exhaust, 02 sensors are all different. If you have a non-CA-PZEV '04 it'll be much easier.
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