Update a record whilst creating a link to a parent record
Change your statement to

UPDATE b
   SET b.ID = a.ID
  FROM tbl_Users        AS a
 INNER JOIN tbl_Absence AS b
    ON a.ID = b.ID
 WHERE b.ID      = 9999
   AND b.deleted = '2019-11-14 10:00:00'
   AND a.ID      = 9999;


(just the first line is changed - use the alias b (for tbl_absence) direct after the UPDATE

PS: the AND a.ID = 9999 is obsolete too, since is implied by the JOIN condition