Line Manager...? I dream of Line Managers.
When I was a lad, we had "Matrix Management".
You'd turn up at work, 3 hours before you left the night before, only to find that the person who was working for you had been assigned by your manager to another manager.
That other manager didn't need that person so had requested the original manager to provide another person. That "another person" was managed by the original person, but as he wasn't needed, he delegated it to you.
You can't do it, as your person has already been assigned to the same project by your manager, even though now he's not needed, so you have to delgate it to your person, who you don't have anyway as he was assigned by your manager to a job that he isn't required for.
So, your person isn't working for you, on a job he isn't needed for and even though nobody's happy with the situation, as you were the last person to assign the person to the job he isn't needed for, beause you can't do it because he's been assigned to that job by your manager, it's all your fault!