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If a new engine was put in the car by a previous owner 6 months ago, is it still covered by the new owner?

It all depends on the terms of the warranty.
You say this was a NEW engine. If that's the case (ie; bought brand new from a vehicle manufacturer such as Toyota, Audi etc), then the factory would normally provide a warranty of 12 months, which should be transferable.
If it was only a second hand engine, most second hand engines have a 3 month warranty.