If, after having signed the new HoYD and the bug occured, I sign a new DoF, it get fixed. I guess again that this is because in the intermediate step in which the old DoF is sacked the new HoYD overwrites him as HoYD.
Hence, when I said in my original post that the issue did not occur the first time I changed HoYD, it may be wrong as I did then also change the DoF, which may have fixed the bug without me noticing it.
Therefore, as a workaround, IF we are anyway replacing the HoYD and the DoF, it seems that the DoF should be the last to be replaced.
But, for example in the save I have uploaded, I may have no wish to change my DoF. It would be great if you already confirm that if I sign Fages as HoYD it is actually him who will be in charge of youth intake despite DoF Bakero being then named instead of him in the Development Centre.