AQP

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?