Log4J: How do I redirect an OutputStream or Writer to logger's writer(s)?

I have a method which runs asynchronously after start, using OutputStream or Writer as parameter.

It acts as a recording adapter for an OutputStream or Writer (it's a third party API I can't change).

How could I pass Log4J's internal OutputStream or Writer to that method?
...because Log4J swallows System.out and System.err, I was using before.