I suppose if anyone knows where Vader’s TIE is located on the Death Star wreckage it’d be Kylo Ren, but it wasn’t seen or mentioned past A New Hope.
We also see Vader arrive on the Second Death Star in a shuttle, no indication that his custom TIE is there at all. Bringing it back for this seems highly coincidental, much more suited for the unedited sequel trilogy than the HAL version.