Ulf,
Are you using the latest version? There is an ajax user/volunteer search function now that allows you to find and sign-up for others easily from the front end (when you are logged in as admin or sign-up sheet manager now)… if you now do it that way, it will store the correct user id for the person that you sign-up for the form, and then the task and clear link will show on their list when they are signed in to their user account.
Just start typing in the first name or last name field of the sign-up form while you are logged in, and you’ll see some results pop under that you can select (if there are any matches).