You might try having someone press down on the rest while you raise it.
I had the same problem after I had sheepskins installed (they had to
remove the head rests first) and it seems to snap into place.
To remove the head rest you need to raise it up and a notch that is not
visible at the back had to be pushed to release it. If the headrest is
forced the plastic part that hold the headrest can be broken. If that is
the case you can open the back part of your seat and replace it. Cheap way
to fix it is using either a tie wrap or metal wire to hold it, but you will
not be able to remove it.
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