If there is a difference between the POH & engine manual, I'd follow the POH.
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POH is the related to both engine & airframe combination.
Very wise.
There can be differences and contradictions between engine and airframe manufacturer's manuals. In aircraft approved before the format of these manuals was well established (CAR 3 aircraft) the statement"... or as stated in the aircraft manufacturer's manual" was not always in the engine manual. Newer manuals generally have something like that. This should be taken as the "tie breaker" to direct you to the aircraft manual as the highest authority.
Other manuals can exist, and indeed supersede the aircraft manual, if it is approved by the authority. Be very cautious of the many other documents out there which offer all kinds of advice and instruction on operating engines. Some are useful, some not so much. If they are "approved" they will be associated with an STC or similar approval, and distinctly marked as such.
It is very likely that the national regulations governing the operation of aircraft state a requirement that the pilot operate in accordance with the "approved" manual(s) for the aircraft. That does not mean that you can't use extra wisdom you have, and perform extra checks and operations, but if those contradict or circumvent the approved information, you're on thin ice as the pilot if something goes wrong. No one's going to get upset if you mag check at 2000 RPM rather than 1800, but dramatic deviations and subsequent difficulties can attract unwanted attention.
In some cases, an operator wants to deviate from what the manual says. (Airlines sometimes do this). In such cases, they will usually obtain a Flight Manual Supplement from the aircraft manufacturer, or have their operation specifically approved by the authority. This is very rare for GA aircraft.