There seems to be a discrepancy in what happens to CoA in the first step of the carnitine transport:

1. Some sources show, that CoA gets released in cytoplasm, while acyl-carnitine is transported to the intermembrane space

2. In other sources, acyl-CoA gets transported as a whole, and free CoA is left in intermembrane space.

Does anyone know which version is correct?

I've been trying to find out more about this, and the second option seems more supported, but what I don't understand is if CoA is released in intermembrane space, what happens to it afterwards? Is there a transport that moves it back to cytosol?

I am not sure that a transporter in the outer membrane would be needed, owing to the presence of porins in the outer membrane.

Lehninger's Principles of Biochemistry seems to indicate that it's left in the cytoplasm. I couldn't tell you anything definitively, but that's the most popular biochemistry book on the market and the one that's consistently highly recommended.